f9c6debb No.3717706[Last 50 Posts]
Regardless of culture, race, sex, gender or creed; humanity survives on it.
The Story of (almost) All Numbers
https://www.youtube.com/watch?v=ggOPJ8gafPo 90f01357 No.3717727
Yeah, well, mathematics in and of itself has nothing to do with racism. Maybe we abstain from identity politics in the math thread?
43198dd9 No.3717734
>>3717712> Math is racistNiggers on average do not have the intelligence to perform advanced mathematics. Certainly there are outliers who may be able to, but they are the rare exception.
> It's also transphobicTranssexuals are by definition insane, and because of that, those pathetic wretches are not able to think clearly enough to do math.
9d6e056f No.3717757
>>3717742reverse mascetomy much
9f0b9328 No.3717793
>>3717750Self-sealing fuel tanks of WW2 used a rubber like material sandwiched between an inner and out metal tank. When punctured, the fuel would cause the material to expand and plug the holes. This is not the same as a self-healing single element material.
f410d12d No.3721589
>>37195861/p per p/s by c^2r relative to the axis or some shit idk
f9c6debb No.3721602
What is Special Relativity used for?
Special relativity is a theory in physics that describes the behavior of objects moving at speeds close to the speed of light. It is primarily used to understand the effects of relative motion, time dilation, length contraction, and the principle of the constancy of the speed of light.
Special relativity is essential for many practical applications and theoretical frameworks, including:
1. Particle accelerators: It helps in understanding the behavior of particles moving at high speeds in particle accelerators like the Large Hadron Collider (LHC).
2. GPS Navigation: Special relativity is necessary for the accuracy of GPS (Global Positioning System) devices. Due to the time dilation effects, clocks on GPS satellites must be adjusted to account for their relative motion to Earth.
3. Nuclear energy: Understanding special relativity is crucial for nuclear power plant operations, as it governs the behavior of particles in nuclear reactors, especially at high speeds.
4. Cosmology and astrophysics: Special relativity plays a critical role in understanding the behavior of objects moving at high speeds in the universe, such as the motion of stars and galaxies, black holes, and the expansion of the universe.
5. High-speed transportation: Special relativity helps in designing and understanding the behavior of high-speed transportation systems, such as trains, planes, and spacecraft. It plays a role in calculations related to time dilation, energy requirements, and relativistic effects.
6. Fundamental physics: Special relativity is an integral part of the overall framework of modern physics. It is essential for understanding and formulating theories like quantum field theory and incorporating relativity into quantum mechanics (quantum field theory being a central framework for understanding the behavior of fundamental particles).
Overall, special relativity is used extensively in a wide range of fields, including physics, engineering, astronomy, and technology, providing a solid foundation for understanding the behavior of objects in motion at high speeds.
f9c6debb No.3721733
How is humanity measured on the Kardashev scale?
The Kardashev scale is a method of measuring the level of technological advancement and energy consumption of a civilization. It was proposed by the Soviet astronomer Nikolai Kardashev in 1964. The scale is based on the amount of energy that a civilization can harness and use.
There are three types on the Kardashev scale:
1. Type I Civilization: This civilization can harness and utilize all the energy available on its home planet. They have mastered the ability to harvest and use all the renewable energy sources on their planet, such as solar, wind, and geothermal power. They can control natural disasters and have a sustainable civilization.
2. Type II Civilization: This civilization can harness and utilize the energy of an entire star or multiple stars within its galaxy. They have advanced technologies that can capture the energy emitted by stars, such as building megastructures like Dyson spheres to capture a significant portion of a star's energy. They have an enormous amount of power at their disposal and can sustain advanced civilizations over long periods.
3. Type III Civilization: This civilization can harness and utilize the energy of an entire galaxy. They can extract the energy from multiple stars, star clusters, or even entire galaxies. Their energy consumption and technology are far beyond comprehension, as they have harnessed the power of cosmic phenomena like black holes, gamma-ray bursts, and dark matter.
It's essential to note that as of now, humanity is not classified on the Kardashev scale, as we have not yet reached a specific level of energy consumption or technological advancement. Some estimations suggest that we are somewhere between a Type 0 and Type I civilization, as we are still heavily reliant on non-renewable energy sources and have not fully harnessed the potential of renewable energy.
f9c6debb No.3721734
How would humanity's logistics steps to build a Type I Civilization?
Building a Type I civilization, according to the Kardashev Scale, would require humanity to harness and utilize energy on a global scale. Here are the logistics steps that humanity might consider to progress towards becoming a Type I civilization:
1. Transition to Sustainable and Renewable Energy: To reach Type I status, humanity needs to shift from fossil fuels to sustainable, renewable sources of energy. This would involve rapidly expanding solar, wind, hydro, and other renewable forms of energy generation, while gradually phasing out reliance on non-renewable sources.
2. Expand Energy Infrastructure: Creating a global energy grid that interconnects various regions and enables the efficient distribution of renewable energy across the planet is crucial. Infrastructure investment would be needed to develop and maintain this energy grid, ensuring reliable and affordable energy access for all.
3. Develop Advanced Energy Storage: To overcome the intermittent nature of renewable energy sources, significant advancements in energy storage technologies would be necessary. This could involve developing improved batteries, exploring new energy storage methods (such as hydrogen or compressed air storage), and optimizing grid management and demand-response systems.
4. Enhance Energy Efficiency: Maximizing energy efficiency in all sectors would be essential. This includes improving energy-efficient technologies, promoting sustainable practices in industries, transportation, and buildings, and educating the public about energy conservation measures.
f9c6debb No.3721735
5. Invest in Sustainable Transportation: Shifting towards sustainable transportation options would be fundamental. This could include transitioning to electric vehicles, expanding public transportation, building efficient and high-speed rail networks, and exploring alternative fuel technologies.
6. Promote Global Cooperation: Building a Type I civilization requires global collaboration and coordination. Governments, organizations, and individuals across the world must come together to pool resources, share knowledge, and work towards common sustainability goals.
7. Focus on Science, Research, and Education: Advancing scientific knowledge and technological innovation is critical. Investing in research and development across various fields, including renewable energy, advanced materials, biotechnology, and space exploration, would enable humanity to progress towards a Type I civilization. Educating the next generation in these fields will also be vital.
8. Address Global Challenges: Overcoming pressing global challenges like poverty, inequality, climate change, and resource depletion is crucial. These issues must be tackled collectively, through international agreements, policies, and initiatives, to ensure a sustainable and inclusive path towards Type I civilization.
These are just some of the logistics steps that humanity may consider in a quest to become a Type I civilization. This endeavor would require significant effort, coordination, and long-term commitment from all societies and nations.
60f597e0 No.3721747
>>3721733i feel like im at a type 4 civilization where none of these rules apply to me at all. so.
d71b90b5 No.3721858
>>3721796Puzzle: given three points randomly placed on a sphere, what is the probability that there is a hemisphere containing all three?
4cf8b748 No.3721996
>>3721733Always thought this scale was kind of useless because all the stages in-between are ill-defined and subjective.
d71b90b5 No.3722248
Math Monday? Learn how to solve this equation in terms of the Lambert W function (product logarithm).
https://youtu.be/mJwfpcXwYRU>>3721996I feel similarly about the Kardashev scale as I do about the Drake equation. Extrapolation from a single data point. Too much uncertainty to be of much use.
f9c6debb No.3723820
There are many reasons why people hate cars; traffic time, self maintenance cost, mental health stress, mechanical injury, workplace abuse, heavy toxic chemicals from cars.
There are many reasons why people like bicycles; healthy, light maintenance, low cost, mental health restoration, little use of chemicals.
1. Traffic time: One of the biggest frustrations with cars is dealing with traffic congestion. Commuters often spend hours stuck in traffic, wasting valuable time that could be used for other activities. Bicycles, on the other hand, can maneuver through traffic more easily, allowing cyclists to enjoy a quicker and more efficient commute.
2. Self-maintenance cost: Cars can be expensive to maintain and repair. Routine services, fuel costs, insurance premiums, and unexpected repairs can quickly add up. Bicycles, on the contrary, have relatively low maintenance costs. Basic repairs and regular tune-ups are more affordable compared to cars, making them a more cost-effective transportation option.
3. Mental health stress: The frustrations of navigating traffic and dealing with road rage can take a toll on mental well-being. Car commuting can often be a stressful experience, contributing to increased anxiety, irritation, and overall mental fatigue. Cycling, on the other hand, offers a more peaceful and enjoyable commute, helping to reduce stress levels and improve mental health.
4. Mechanical injury: Car accidents can lead to severe injuries or even fatalities. The risk of being involved in a car crash is a significant concern for many people, given the high speeds and large number of vehicles on the roads. Bicycles, although not without risk, generally see fewer severe accidents and injuries when compared to cars.
5. Workplace abuse: Some individuals may associate cars with workplace-related stress, such as long commutes or having to use a personal vehicle for work-related tasks. This association can lead to negative feelings towards cars and a preference for alternative transportation methods like bicycles.
6. Heavy toxic chemicals from cars: Automobiles contribute significantly to air pollution through the release of toxic chemicals and greenhouse gases. This pollution adversely affects air quality and poses serious health risks, such as respiratory problems and cardiovascular diseases. Bicycles produce zero emissions and are considered an eco-friendly mode of transportation, leading to cleaner air and a healthier environment.
f9c6debb No.3723822
How massive cars and traffic create homeless and crime rate according to data.
Based on the available data, there is some evidence to suggest a connection between the massiveness of cars, traffic congestion, and the incidence of homelessness and crime rates in certain contexts. Here are some key points:
1. Urban Sprawl: The use of large and massive cars has contributed to urban sprawl, with cities expanding in size and becoming more spread out. As a result, people are increasingly pushed to live farther away from their workplaces, thereby facing longer commutes and increased traffic congestion.
2. Increased commuting costs: Massive cars typically consume more fuel, resulting in higher commuting costs for individuals. This financial burden can lead to increased housing cost burdens, eventually resulting in housing insecurity. When people are unable to afford housing, they may end up living on the streets, contributing to homelessness rates.
3. Lack of affordable housing near employment centers: As cities become more congested with traffic and homeownership becomes increasingly expensive near employment centers, affordable housing options become limited for low-income individuals. This lack of affordable housing can lead to higher rates of homelessness, as people struggle to find secure accommodation within their budget.
-TBC
f9c6debb No.3723824
4. Socio-economic inequality: The impact of traffic congestion and limited affordable housing options disproportionately affects low-income individuals and communities. With limited access to transportation options, they may face difficulties commuting to work or seeking employment opportunities. The resulting joblessness and economic inequalities can contribute to higher crime rates within these communities.
5. Car-centric urban planning: The prioritization of car-centric urban planning, such as dedicating large amounts of space to roads and parking lots, can lead to the displacement of low-income communities. This displacement can perpetuate a cycle of poverty, as affected individuals may struggle to find stable accommodation and employment opportunities.
It is important to note that while some data suggests these connections, variables such as income inequality, social policies, and systemic issues can also contribute significantly to homelessness and crime rates. Therefore, it is crucial to consider these broader factors when examining the relationship between massive cars, traffic congestion, and societal issues like homelessness and crime.
f9c6debb No.3724863
asked
https://talkai.info/chat/MAY NOT BE ACCOURATE RESULTS AND NEED REFINING BY HUMANS.
What if you increase the mass of a wind up spring motor to generate longer lasting electricity?
Increasing the mass of a wind-up spring motor would not directly increase its ability to generate longer-lasting electricity. Here's why:
1. Energy storage: The spring in a wind-up motor acts as an energy storage device. When you wind it up, potential energy gets stored in the spring. As the spring unwinds, this potential energy gets converted into kinetic energy that can power the motor. Increasing the mass of the spring might enable it to store more potential energy, but it wouldn't extend the total energy available.
2. Conversion efficiency: During the unwinding process, some energy is lost due to various factors like friction, heat, and inefficiencies in the motor. Increasing the mass of the spring does not necessarily improve the conversion efficiency of converting potential energy into electricity. In fact, it might even increase losses due to increased friction.
3. Power output: The power output of a wind-up spring motor depends on the rate at which the spring unwinds (angular velocity). Increasing the mass of the spring could potentially decrease the unwinding speed, resulting in a lower power output.
To generate longer-lasting electricity, you would need to focus on improving the efficiency of energy conversion, reducing frictional losses, or increasing the capacity of the energy storage system (e.g., using a more efficient battery).
f9c6debb No.3724864
>>3724863What would it take for a wind up spring motor to match the energy output as a car battery?
To match the energy output of a typical car battery, which typically has a capacity of around 50-70 ampere-hours (Ah) at 12 volts (V), a wind-up spring motor would need to be able to store and release a similar amount of energy.
One way to estimate the required energy storage capacity is to calculate the total energy stored in a car battery (Watt-hours) using the formula:
Energy (Wh) = Voltage (V) * Capacity (Ah)
For example, let's assume a car battery with a capacity of 60 Ah:
Energy = 12 V * 60 Ah = 720 Watt-hours (Wh)
Now, let's assume a typical efficiency of 90% for a spring motor (due to energy losses from friction and heat):
Energy required for the wind-up spring motor = 720 Wh / 0.9 = 800 Watt-hours (Wh)
To store 800 Wh of energy, the spring motor would need to have a mechanism capable of storing and releasing this amount. The specific design and size of the spring motor would depend on factors such as the efficiency of the mechanism and the type and size of the spring used.
However, it's important to note that matching the energy output of a car battery with a wind-up spring motor can be quite challenging due to the relatively low energy density of mechanical energy storage systems compared to chemical batteries. Moreover, the practicalities of transferring mechanical energy from a wind-up spring motor to perform work in a vehicle would require further considerations like the overall weight, size, and efficiency of the system.
d0203366 No.3724872
>>3724044>actually solved the statics problem correctly. But their conclusion that tendons can't sustain this tension is wrong.The problem still remains, since that's the static load from just crouching down like that. The human Achilles tendon exceeds that load briefly during dynamic loading, and as the paper states: "yet despite its tremendous strength, is frequently injured.". If you put that static loading on a human Achilles tendon for any extended period of time, it would cause a stress injury and eventually rip it - yet that's exactly how this creature normally stands. As soon as that fox thing tried to move and jump…
d0203366 No.3724875
>>3724044There's additional problems as well. If you want to think of it in terms of suspension systems, you need a 2900 Newton pre-load before you even consider the dynamic loading. Since the tendons act as springs, and springs need to stretch to generate forces, that leg would be extremely funny to walk on.
A human standing flat on the foot has a pre-load of zero at the Achilles tendon. Our knees lock up, so our legs turn into rigid stilts and we only need to apply slight corrections to keep from tipping over.
d0203366 No.3724884
>>3724864It's interesting that the AI didn't do a simple wikipedia search for energy density.
Clock springs have an energy density of 0.0003 MJ/kg so 800 Watt-hours translates into 9600 kg of spring steel.
9449b918 No.3724894
>>3724884The AI doesn't care about truth. Remember the incident where a lawyer used AI to produce court filings. On the surface the documents seemed proper and legitimate. The AI fabricated six nonexistent court decisions, however.
https://arstechnica.com/tech-policy/2023/05/lawyer-cited-6-fake-cases-made-up-by-chatgpt-judge-calls-it-unprecedented/ f410d12d No.3724913
>>3724863There are a few ways to exploit this.
The fastener pin can be copper wound iron rod. It can work as a coiled-copper-tubing to produce more power. These can be enhanced and compact but given the small space in which it is used is limited.
The module will take any electro magnetic field made from the placeholder rod and colllect it directly. It helps to have a piston motion of the rod as well. Or a direct motion that generates the electric field (such as the rod being used as a loop)–this limits the design of the model somewhat to rely on a locked ringed-tube-pin. However, Many more modules in a "flywheel" can also collect on the same field that is generated. Maybe?
The pin-fastener rod being exploited is really the main goal. As the spring unwinds it allows a piston like motion to occur over its placeholder. This is made better that forward/reverse motions all generate power. As the spring must be rewound, it can be exploited that the rod can be used to incrementally wind the spring back. This requires a steplock of some sort that it can do so, this also requires a trigger release to allow the spring to be rewoundm these can be handled as seperate mechanisms like a clutch. The clutch will lock the rod into a directional movement, the piston motion of the rod will allow the spring to be rewound incrementally, the release trigger can be set to allow an optimal schedule for the spring to be unwound, allowing for the most of a powerdraw per this cycle. Maybe…
The longer the pathway of the rod being used, the more modules can be used to harness an electromagnetic field over, and charge a battery to allow these mechanisms to be used robotically. Then simply wind the spring and release it over a flywheel of modules connected all by the same rod with as many spring/power modules connect to it to generate enough power for everything.
f9c6debb No.3724916
>>3724913Applications -
10-16 hour battery supply
low powered communications.
Radios low powered tv sets video hand held game boys and generation counsels
f410d12d No.3724922
>>3724916A gaussian particle beam (or a ballistic pipe cleaner, passing through a coil) can likely net a 70% power return. So at maximum efficiency the spring can net a 70% power return with additive components like solar or a component piston rod/toroid-ring/hotwire-tube would net a 10 hour or so battery charge. For Dedicated power recycling. I am basing this on of course no evidence and I am not doing the complicated math for it at 4 in the morning or any other time.
f410d12d No.3724923
>>3724922Basically a microwave powered spring load at some reduced output overall. Adding a belt driven alternator and transmission and drive chain and power train will assist as well. Converting to a canister fed super collider that launches hi-velocity vacuum-chambers that create giant emp fields would be the actual thing to do here. Anyways I am going to go back to in-home horticulture and virtual lasic surgery. Since we live in that age.
12b93989 No.3725652
Soviet Era Mathematics
https://www.youtube.com/watch?v=LlsA7hygaVoAdvanced mathematics can be used in farming climate season weather logistics in various ways. Here are a few examples:
1. Predictive modeling: Advanced mathematical models can be used to analyze historical weather data, including temperature, rainfall, wind patterns, etc. These models can help in predicting future weather patterns and seasons, enabling farmers to plan their crop rotation, irrigation, and pesticide schedules accordingly.
2. Decision optimization: Mathematical optimization techniques can be used to optimize decisions related to planting, harvesting, and resource allocation on farms. Farmers can use mathematical algorithms to determine the optimal time to plant different crops based on climate predictions, ensuring maximum yield and efficient resource management.
3. Irrigation management: Advanced mathematics can be used to develop sophisticated irrigation scheduling systems. Mathematical models can consider factors like soil moisture, evapotranspiration rates, weather forecasts, and crop water requirements, helping farmers optimize irrigation scheduling and reduce water wastage.
4. Pest and disease management: Mathematical models can be used to simulate the spread of pests and diseases based on weather conditions. These models can help farmers develop effective strategies to prevent and control outbreaks, optimize pesticide and fungicide application schedules, and minimize the economic and environmental impact of these treatments.
5. Crop yield estimation: Advanced mathematical techniques, such as statistical modeling and machine learning, can be used to predict crop yield based on climate data, soil quality, and other relevant factors. Accurate yield estimation helps farmers make informed decisions regarding resource allocation, marketing, and overall farm management.
By harnessing the power of advanced mathematics, farmers can optimize their farming practices, mitigate risks associated with climate variability, reduce input costs, and ensure sustainable agricultural production in the face of changing weather patterns.
0d8c32fe No.3727512
>>3727473The Bible doesn't care much for math, either. IIRC, there is a passage describing the "molten pool" at Solomon's temple which says it was "round in compass" and ten cubits across but also thirty cubits in circumference.
I guess pi must equal 3 according to the Bible.
12b93989 No.3727587
https://www.reddit.com/r/fuckcars/comments/y94xqa/downtown_providence_ri_1937_vs_2022_fuck_cars_but/?rdt=61140In the United States; Why are there more long highways roads for cars than rails for train transportation?
Reason why? Over saturation of cars have flooded the area and there are lack of trains and bikes that could balance and improve time and economic logistics what are your thoughts on this?
12b93989 No.3727588
There are several reasons why the United States has more long highways for cars compared to rails for train transportation:
1. Historical Factors: The development of the United States' transportation network has been closely tied to the growth of the automobile industry. The country experienced a significant boom in car ownership and usage following World War II. As a result, the highway infrastructure was greatly expanded to accommodate the increasing number of vehicles, while investment in railroads declined.
2. Geographic Factors: The vast size and relatively lower population density of the United States make highway transportation more practical than rail. Highways can reach remote areas and provide door-to-door convenience, while rail networks require substantial investments and may not be financially viable in less developed regions.
3. Flexibility and Accessibility: Highways are more flexible in terms of routes and destinations. They allow individuals to travel directly from their point of origin to their desired destination, offering convenient access. Rail systems, on the other hand, often require multiple transfers and may not have stations in proximity to every desired location.
4. Cargo Transportation: While rail transportation is efficient for bulk freight and heavy goods over long distances, the United States relies heavily on trucking for the majority of its cargo transportation. Trucks provide more flexibility and allow for just-in-time deliveries, making them more suitable for the country's extensive supply chain and logistical requirements.
5. Limited Investment in Rail: The United States has historically invested less in rail infrastructure compared to countries with extensive passenger and freight rail networks, such as those in Europe and East Asia. Limited government funding and a lack of political will have hindered the expansion and modernization of the country's rail systems.
While the over-saturation of cars and lack of alternative transportation options can contribute to congestion and inefficiencies, it is a complex issue that requires substantial investments, planning, and shifting societal preferences to promote a more balanced and sustainable transportation system.
9a3823aa No.3727593
>>3727512For Bible-thumbers who technically believe in a magical global Santa rewarding people for being naughty or nice , i would think pi=3 is close enough for ANY purpose they would ever use math/critical thinking about cause and effect or natural laws.
7f199b3a No.3727594
>>3727588>>3727587The left's obsession with restricting the free movement of the populous to state controlled transport is a subject for the pol thread, not the math thread.
12b93989 No.3727597
>>3727594Was asking chatGPT and it said this.
548df0a0 No.3728242
>>3728239
Some urbanite soyboy made that chart. Fuck living in cities and fuck being forced onto a cattle car with the dregs of society
05c2a49b No.3728684
>>3728676The old adage, "Money is the root of all evil," is in fact a vainglorious misdirection of the true source of evil. As money is nothing more than a construct, mankind is the root of all evil. On the tier of moral existence, cockroaches are more moral beings than humanity. They only eat each other when there's nothing else to eat, whereas humanity devours itself daily by exploitation under the law and criminal behavior outside it. HEre's hoping humanity nukes itself or an asteroid does to us what it did to the dinosaurs. We're a cancer limited to the earth and the galaxy needs to exercise its immune system and wipe us out before we spread.
136631f2 No.3730584
>>3730582THH
> What is the probability that each winsOne chance out of eight?
5ae7728f No.3730652
>>3730584depends on virtually or not. depends on if you are in a simulation or not. depends on some really deep shit. you might just be self gratifyingly pragmatic and in a simulation that has you convinced everything works out but in reality consequences killed jfk
e386e95c No.3730660
>>3730582>>3730613Since the coin has no memory of previous throws, every equal length sequence of flips is equally likely: 1:8.
Thinking that TH- is more likely to come before HH- or TT- is the good old Gambler's Fallacy.
fe33ae6b No.3730689
>>3730582>>3730613>>3730660These posts remind me of the old
Monty Hall Problem.https://blogs.scientificamerican.com/observations/lets-make-a-deal-revisiting-the-monty-hall-problem/"Charles Sanders Peirce once observed that in no other branch of mathematics is it so easy for experts to blunder as in probability theory."
5ae7728f No.3730730
>>3730693not accounting for all permutes instills bias. TTH/HTT
??? has 100% chance of and not of. This could be considered unimportant information maybe. Permute this and its suddenly semi-important.
Generally ??? is also 99% an origin of NULL and 1% H:T
99(everything that isn't h:t or isn't "yet"):(everything that is h:t or "already is")1
Permute this and you have dividers of anything that isn't the resulting answer compared to the resulting answer. Makes the case for the resulting answer to be profoundly impossible and now 0%.
d71b90b5 No.3730847
>>3730582>>3730613Found a spare moment to explain this. To recap,
probability THH occurs first: 3/4
probability HHT occurs first: 1/4
The major insight is the realization that the only way for HHT to occur first is if it is preceded by a string of "H"s e.g. HHHHHHHT. So the probability of getting HHT in the 1st three flips is of course 1/8. The probability of first getting HHT on the 2nd, 3rd, and 4th flips i.e. the probability of getting HHHT is 1/16 and so on. So the total probability of HHT occuring first is the sum of the probability of getting each of these sequences, HHT, HHHT, HHHHT, and so on:
probability of HHT first = 1/8 * (1/2^0 + 1/2^1 + 1/2^2 + 1/2^3 + 1/2^4 + …) = 1/4
This is just a geometric series, which sums to 1/4. So the remaining probability goes to the case THH occurs first, 1 - 1/4 = 3/4. If it's not obvious why the case of THH occurring first absorbs
all the remaining probability, think it over some more. But a significantly more involved analysis reveals the series for this probability too.
probability of THH first: 1/8 * (1/2^0 + 2/2^1 + 3/2^2 + 5/2^3 + 8/2^4 + …) = 3/4
Note the Fibonacci numerators.
e386e95c No.3730848
>>3730847> the only way for HHT to occur first is if it is preceded by a string of "H"s e.g. HHHHHHHT.You can also get THTH… or HTHT… indefinitely before you get into HH… or TT…
e386e95c No.3730849
>>3730847Also, because there's no special meaning to H or T, you can swap them around and you should be able to make the same claim.
So the probability of HHT or TTH must be symmetric. One cannot be more probable than the other.
d71b90b5 No.3730860
>>3730848Okay, let's use your examples. What happens when we tack HHT onto the end?
THTHHHT
HTHTHHT
Now ask yourself, does HHT occur first in these strings? Take all the time you need.
e386e95c No.3730864
>>3730860You forget other possibilities.
THTH…HHT
THTH…TTH
HTHT…HHT
HTHT…TTH
All of these are equally likely to occur.
e386e95c No.3730865
>>3730860And, since they're just two sides of the coin arbitrarily assigned a name, the sequence:
THTHHHT is the same as HTHTTTH
It's just a matter of which side you consider to be heads or tails. Since this choice is arbitrary and doesn't depend on the coin or the throw, it must be that both outcomes TTH and HHT are equally likely. The coin cannot behave differently simply by you choosing which side is the Heads.
e386e95c No.3730866
>>3730864To expand to all permutations:
THTH…
HTHT…
TTTT…
HHHH…
All those have equal probability, and the next throw is independent, so the possible outcomes of the next throw are:
THTH… T
THTH… H
HTHT… T
HTHT… H
TTTT… T
TTTT… H (TTH)
HHHH… T (HHT)
HHHH… H
Both TTH and HHT are equally likely to come up on the next throw. The probability is 1/8.
e386e95c No.3730867
And again if you don't believe it, the possible outcomes, assuming you didn't get either one on the last throw are:
THTHT T
THTHT H
THTHH T (HHT)
THTHH H
HTHTT T
HTHTT H (TTH)
HTHTH T
HTHTH H
TTTTT T
TTTTT H (TTH)
HHHHH T (HHT)
HHHHH H
Two and two out of 12, which makes the probability to get HHT or TTH equal at 1/6. You can continue adding throws, and it becomes more and more likely you'll eventually get HHT or TTH, and they will always have equal probability.
5ae7728f No.3730878
You have 100% of one or the other occuring, assuming one or the other has occured that the next resulting occurence is either or of a 100% symmetrical difference. But also that either one variable or the other indicates itself or the other in its place. Everytime any instance of a variable occurs it denotes thousands of other results having occured in its place. That Each integer of that variable denotes an infinite possibility of arrangements for which each integer represents. Being that the chance for either to occur is infinite compound by its exampled string being infinite. With 100% data compression it actually never happened therefore its 0%.
5ae7728f No.3730882
>>3730880((((0/∞/∞/∞)/∞)/∞)/∞) chance
5ae7728f No.3730883
>>3730882((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞) expanded chance (formatting infinity to match zero chance) (0% chance defined by infinite zeros of itself) Or absolute zero by absolute infinity).
5ae7728f No.3730884
50/50 chance for either H or T:
1/
((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)
/
((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)
that either or variables occur
5ae7728f No.3730885
For HHT or TTH
1/
((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)
/
((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)
/
1/
((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)
/
((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)
/
1/
((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)
/
((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)
For specifically HHT or TTH to occur between themselves.
1/
((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)
/
((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)
/
1/
((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)
/
((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)
/
1/
((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)
/
((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)
actually i know this is wrong because both could happen so its actually.
1/
((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)
/
((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)
/
1/
((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)
/
((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)
/
1/
((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)
/
((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)/((((0/∞/∞/∞)/∞)/∞)/∞)
i dont care really maybe its funny to you or something.
5ae7728f No.3730979
>>3730978they speak in numbers
d71b90b5 No.3731050
>>3730847Explanations should be as simple as possible, but no simpler.
If you get heads on the first two flips, you are guaranteed to get HHT before THH. Because the chance of starting with HH is 1/4, this is the same probability of getting HHT first. The remaining probability of 3/4 is that of running into THH first.
9d6e056f No.3731073
>>3731050Ultimately depends if the universe is good natured or not. this is a light-wave issue of what is observed as heads or tails. If you live in a world where light is opposed to your existence it will bely the answer, that heads is actually tails and tails is actually heads. What you get depends simply on the end resulting in favor to heads or tails, not whether or not that is true.
e386e95c No.3731083
>>3731050> The remaining probability of 3/4 is that of running into THH first.No it's not. Two of the four possible throws, TH and HT may end with HHT with subsequent throws.
9d6e056f No.3731102
>>3731080if h or t were pressure sensitive then appliance of pressure would indicate h or t based on sheer chance h or t occur of a change of pressure (or are they both attracted to pressure and therefore for every instance there is an h there is also a t)
21d2d39d No.3731305
Math Monday, nerd bitches! That means pencils down for last week's puzzle, but pick them right back up for this week's new puzzle. Congrats to
>>3730613 for solving last week's puzzle. Here's the solution the author posted this morning along with your new challenge.
https://gizmodo.com/gizmodo-monday-puzzle-ugly-ducking-big-bad-wolf-1851191302Puzzle #28: Duck Duck Go
The Ugly Duckling is in the center of a circular lake when he spots the Big Bad Wolf lurking on the shore. The wolf cannot swim, and the duckling cannot fly away from water (but can fly from land). The wolf patrols the outside of the lake waiting for the duckling to reach land so that he can feast. The wolf moves four times faster than the duckling can swim. He can see the duckling and is free to prowl along the shoreline however he wants. How can the duckling make it to land and fly away without becoming the wolf’s dinner?
As usual, this isn’t a trick question. The answer isn’t “the lake is frozen so the duckling can fly away” or anything like that. There is a legitimate strategy with mathematical reasoning behind it. Good luck!
e386e95c No.3731309
>The wolf moves four times faster than the duckling can swim.
So 500% the speed?
The longest path that the wolf has to take around the lake is pi x radius. Since the difference between pi x radius and radius is less than four times the radius - which is also how much faster the wolf is - the wolf can always catch up to the duckling. It can reach any point along the shore faster than the duckling can swim away from the center.
The "trick" only works if the wolf is less than pi times faster than the duckling, so the duck can trick the wolf to wait at the opposite side of where they're trying to swim.
e386e95c No.3731311
>>3731305Of course, the "mathematical" answer is something like aiming a certain number of degrees ahead of the wolf to maximize their running distance, but since we're dealing with a duck that can do math, we're also dealing with a wolf that knows the trick and simply switches direction, forcing the duckling to turn back the other way.
5ae7728f No.3731352
>>3731305wait until wolf sleeps the end. stupid question
5ae7728f No.3731353
>>3731305midmaxing coast-to-shore footing differences until flight is achievable while dodging wolf counter steps. the end.
93000494 No.3731492
https://imgur.com/gallery/4vcJ2dNThen this just happened to their rental while they were home, they went out on the front porch from their bedroom because they heard branches cracking then this happened. My grandchildren were inside along with 2 dogs and 2 cats. Amazingly nobody was seriously hurt. Another person in a home down a ways away wasn’t as fortunate. Emotionally we’re all a mess. The tree ripped through their bedroom.
I know it sad; but what if they hired carpenters to cut parts of the fallen tree into planks and rebuild the house with it?
how much time, tools, and labor would it cost?
5ae7728f No.3731499
>>3731457IF wolf stuck facing one way den you just go it the other way.
09957c0f No.3731548
>>3731535You know i just don't have the math on me right now.
some delta or phi/pi degree probably? really though it should be independent from the original shape and its own formula.
for me personally orbitals seem to substitute this pretty well. I have pretty much never needed to skew something and imo a true-skew it only exists as an exact mirror image to something else. for computers its like isolating an objects through a quarantine or using a filter.
I am sure you can prove it.
09957c0f No.3731550
>>3731548A linear or quantum skew might also be important. I think that it shows more being as an internal/external drawpoint (once you skew something the direction is important). Drawpoint for a whole formula with as its own radian, i think that describes the next step as long as they stay(or are also dependent) on a superaltive legend, you need number maps if its more than one dimension. I am just very busy.
09957c0f No.3731561
>>3731550I think you can just say a vector is a skew actually. Though it helps to also define the vector zeros/limits (constraints too). Really busy.
09957c0f No.3731564
>>3731561you know i think you can use say anything in (parentheses) is skewable by {bracket base skew} and [sub-base skew] then its good to pattern out over a full skew-matrix, that would work with the skew-scope. Before you do anything with it that is, you need all those parts considered to apply a vector. Then just plug it into your function(linear) and prep for quantum-skew patterns. Probably only works with uh, very basic quantum functions that have patterns. It will probably end up getting nulled anyway. Just fyi. I'm super busy and actually don't have a good example.
09957c0f No.3731565
>>3731564not sure deritives will express a skew correctly right so you need to doubledown and have normals differintiated too. There should be a tool for this. I would check wolfram and github or something.
437db414 No.3732102
Math Monday! Looks like no one got last week's puzzle or even made an attempt. Regardless, here's the solution and this week's new puzzles.
https://gizmodo.com/gizmodo-monday-puzzle-super-bowl-1851232384That's right, we got a twofer:
Puzzle #29: A Sporting Chance
I missed the Super Bowl. All I know is that the two teams were perfectly matched in skill (suspend your disbelief) and that the score was not tied at halftime. I want to know the chances that the team who trailed at halftime pulled a comeback to win the game. Given only this information, what should I put the chances at?
By perfectly matched, I mean that the teams have the same probabilities of achieving various scores, and furthermore these probabilities don’t change based on game situation (i.e. which half they’re in or who’s ahead). Remember that Super Bowl games cannot end in ties: If scores are even after the second half, they enter overtime.
Bonus puzzle:
Several teams participate in a simple round-robin tournament (i.e. every team plays every other team once). Call a team a super-winner if every other team in the tournament either lost to them or lost to someone who lost to them. Argue that every tournament has at least one super-winner.
The halftime puzzle might seem like an overly simplistic model of athletic outcomes, but a study on NBA comebacks calculated how often the team that leads at halftime goes on to win the game and arrived at almost exactly the same quantity that this puzzle’s answer predicts. I’ll link the study in the solution next Monday.
42088978 No.3732111
Quadratic Reciprocity
This app provides an introduction to quadratic residues leading up to the Quadratic Reciprocity law. It also implements an algorithm for determining quadratic residues using this law. Further, when this algorithm is run it provides a step-by-step explanation of the results.
While a grasp of some advanced math is required to fully appreciate the quadratic reciprocity law, at one level it can be understood in terms of elementary number theory. Our goal is to make this exposition accessible to both levels of readers.
The app makes use of Latex and MathJax to present the mathematics with standard notation, and uses the app's programming capabilities to implement the algorithm. It does not require an internet connection and works completely offline.
https://play.google.com/store/apps/details?id=com.realandcomplexsoftware.quadraticreciprocity d71b90b5 No.3732394
>>3732102Last Week's Puzzle #28Here's the video I mentioned that better explains the solution:
https://youtu.be/vF_-ob9vseMThis Week's Puzzle #291/4 probability that the team who trailed at halftime pulled a comeback to win the gameI reasoned by analogy using coin flips and came up with 1/4. This may have been the wrong approach, but it makes sense to me.
Bonus PuzzleIf there are just two teams, clearly one will be the super-winner. Given a group of three teams, there's either one team that beats the other two (
one super-winner) or they form a cycle like in rock-paper-scissors (
three super-winners). Add another team, and if they lose to a super-winner from the previous three matches, then the previous super-winner retains their title. If the newly added team wins against all previous super-winners, then that team becomes a super-winner. This kind of inductive reasoning shows that no matter the size of the tournament (number of teams) there will always be at least one super-winner.
aedd6817 No.3732734
Math Monday!
>>3732394 solved last week's puzzle.
https://gizmodo.com/gizmodo-monday-puzzle-survivor-challenge-flags-1851232495Puzzle #30: Survivor Flags
Jeff Probst has planted 21 flags in the ground. Tribe A and Tribe B will alternate removing either one, two, or three flags at a time (zero is not allowed). The tribe that removes the last flag wins. If Tribe A goes first, which team can force a win and what is the winning strategy?
04029fb2 No.3732747
>>3732734This is a famous game in disguise and is pretty easy to reason out, so I'll leave it for others and just mention a sneaky trick that Harry Anderson described in Games You Can't Lose:
One way to con people with this game is simple sleight of hand. You let your opponent maneuver you into a losing position, then when you go to take a 'flag' from a pile, you simultaneously drop a palmed flag into the pile, thus ruining their count. When they are sure that they are screwing you over, they are less likely to be counting accurately…
d71b90b5 No.3732792
>>3732734If Tribe A goes first and utilizes the optimal strategy, they will win.
The optimal strategy is to remove only one flag on the first move. This forces Tribe B to pick from 20 remaining flags. B cannot remove enough flags so that A must pick from 16 remaining flags, but A can force this upon B on their turn. A can continue to force B into situations in which they must choose from a number of flags divisible by 4. Until B chooses from 4 remaining flags, at which point A claims victory on their subsequent move.
5d53053b No.3733063
>>3733061calculation follows this logic examples;
1.000 to 1.999 hits to 2.000
1 Swift Nectar is L$2.800 how much is for 100 Swift Nectars?
5d53053b No.3733069
>>3733063My standard calculator says to buy swift nectar price is 2.8 and if I buy 100 the price would be L$280 does that sound correct?
5d53053b No.3733072
United States Currency $18.1250 = Price L$5.800 x Flash Nectar 1000 = Price L$5,800
5d53053b No.3733073
Original $1 currency does not change it's own value but printing copies inflation value on other nations foriegn currencies does change their value.
013ab6bb No.3733376
Math Monday! Way to go
>>3732792 for solving last week's puzzle.
https://gizmodo.com/gizmodo-monday-puzzle-hipe-word-game-1851269529Puzzle #31: HIPE Me Up
For each string of letters, find a word that contains that consecutive letter sequence.
BV
WKW
ONIG
SPB
RAOR
HQ
TANTAN
PTC
GUAG
d71b90b5 No.3733511
>>3733376Puzzles for normies. This one's not even math.
BV →
obviousWKW →
awkwardONIG →
tonightSPB →
raspberryRAOR →
extraordinaryHQ →
earthquakeTANTAN →
instantaneousPTC →
bankruptcyGUAG →
language>>3733396Hellhound ate my homework. A years worth of homework.
4cb9d9b3 No.3733688
>>3733686Now find an easy solution to theTravelling Salesman Problem so Amazon can deliver stuff with the least miles driven.
>>3733680Interesting, the Dutch appear to have completely avoided North America in 1850. I guess they still remembered the spanking Holland got from England a century or two earlier. :)
5d53053b No.3733701
>>3733688One possible solution to the Travelling Salesman Problem for Amazon would be to use a heuristic algorithm such as the nearest neighbor algorithm. This algorithm involves starting at a random point and selecting the nearest unvisited point as the next destination until all points have been visited. This can help minimize the distance traveled and optimize the delivery route for Amazon. Additionally, implementing route optimization software or utilizing real-time traffic data can further improve the efficiency of delivery routes.
5d53053b No.3733702
>>3733688Indeed, the Dutch had established some colonies in North America during the early 17th century, such as New Netherland (which included parts of present-day New York, New Jersey, Delaware, and Connecticut). However, due to conflicts with the English and other European powers, they eventually lost control of these territories. By 1850, the Dutch had largely shifted their focus to other regions and did not have a significant presence in North America. It's possible that the memory of past conflicts with the English played a role in their decision to avoid further colonization in North America at that time.
9d6e056f No.3733704
>>3733686>>3730582already know that but that is also not the final answer.
9d6e056f No.3733705
>>3733701human ships implying humans share information but not via interacting via built-in intrinsic heuristics because humans propagate like viruses. so makes for human driven quantum science being the deathblow for humans at all.
5d53053b No.3733706
One plus one equals one bigger one.
This is not correct. One plus one equals two.
One plus one equals one bigger one because if you have two ones you merge it into a single one.
This is not accurate mathematically. One plus one equals two in a traditional sense. When you add one and one together, the sum is two.
How do you combined two ones into one?
You can combine two ones into one by simply adding them together.
1 + 1 = 2
So, by adding two ones together, you get a total of two.
So basically 2 has become a bigger one.
In a sense, yes. When you add 2 to 1, you get a larger number, making 2 a bigger quantity than 1.
5d53053b No.3733709
>>3733705This statement seems to suggest that human ships, or perhaps the way humans communicate or share information, lead to negative consequences because humans reproduce rapidly and spread like viruses. It implies that humans' behavior in the realm of quantum science could ultimately be detrimental to themselves.
It's possible that the author is expressing concerns about the rapid advancements in technology and the potential consequences of humans' actions in the realm of quantum science. The comparison to viruses may suggest a negative impact on the environment or on humanity itself.
Overall, the statement raises questions about the ethical implications of human actions and advancements in science and technology, and the potential risks involved. It emphasizes the importance of considering the consequences of our actions and the need for responsible decision-making in the pursuit of scientific knowledge.
5ae7728f No.3733723
>>3733709It seems you're looking for a conceptual implementation of a system that might be part of a science fiction narrative, where human ships share information in a non-traditional way, and this sharing mechanism is related to quantum science which poses an existential threat to humanity. This is a highly abstract concept, but I can create a Python simulation that might represent a simplified version of this idea.
We'll create a simulation with the following components:
- `Ship`: A class representing a human ship that can share information.
- `QuantumChannel`: A class representing a quantum communication channel.
- `Humanity`: A class representing the collective of human ships.
- `QuantumEvent`: A class representing a quantum science event that could be a threat to humanity.
- `Simulation`: A class that runs the simulation and determines the outcome.
Let's start by creating the entry point file which will run the simulation.
main.py
```python
from simulation import Simulation
def main():
# Initialize and run the simulation
simulation = Simulation()
simulation.run()
if __name__ == "__main__":
main()
```
Now, let's define the `Ship` class.
ship.py
```python
from dataclasses import dataclass
@dataclass
class Ship:
"""
Represents a human ship with the ability to communicate via a QuantumChannel.
"""
name: str
quantum_channel: 'QuantumChannel'
def share_information(self, info):
"""
Shares information with other ships via the quantum channel.
"""
self.quantum_channel.transmit(info, self)
```
5ae7728f No.3733724
>>3733723Next, we'll define the `QuantumChannel` class.
quantum_channel.py
```python
class QuantumChannel:
"""
Represents a quantum communication channel used by ships to share information.
"""
def __init__(self):
self.subscribers = []
def subscribe(self, ship):
"""
Subscribes a ship to the quantum channel.
"""
self.subscribers.append(ship)
def transmit(self, info, origin_ship):
"""
Transmits information to all subscribed ships except the origin ship.
"""
for ship in self.subscribers:
if ship is not origin_ship:
# In a real quantum channel, this could be an instant process
# Here we simulate it as a method call
ship.receive_information(info)
def unsubscribe(self, ship):
"""
Unsubscribes a ship from the quantum channel.
"""
self.subscribers.remove(ship)
```
5ae7728f No.3733725
>>3733724The `Humanity` class will manage the collective of ships.
humanity.py
```python
from ship import Ship
from quantum_channel import QuantumChannel
class Humanity:
"""
Represents the collective of human ships.
"""
def __init__(self):
self.ships = []
self.quantum_channel = QuantumChannel()
def add_ship(self, name):
"""
Adds a new ship to the collective.
"""
ship = Ship(name, self.quantum_channel)
self.ships.append(ship)
self.quantum_channel.subscribe(ship)
def remove_ship(self, ship):
"""
Removes a ship from the collective.
"""
self.ships.remove(ship)
self.quantum_channel.unsubscribe(ship)
```
The `QuantumEvent` class will represent a quantum science event.
quantum_event.py
```python
class QuantumEvent:
"""
Represents a quantum science event that could be a threat to humanity.
"""
def __init__(self, severity):
self.severity = severity
def impact(self, humanity):
"""
Determines the impact of the event on humanity.
"""
# The impact logic can be complex, here we simulate a simple version
if self.severity > 50:
return "Catastrophic impact! Humanity is at risk."
else:
return "Manageable impact. Humanity survives."
```
Finally, the `Simulation` class will run the simulation.
simulation.py
```python
from humanity import Humanity
from quantum_event import QuantumEvent
class Simulation:
"""
Runs the simulation of human ships sharing information and facing a quantum event.
"""
def __init__(self):
self.humanity = Humanity()
self.quantum_event = QuantumEvent(severity=75) # Arbitrary severity level
def run(self):
# Add some ships to humanity
self.humanity.add_ship("USS Enterprise")
self.humanity.add_ship("USS Voyager")
# Simulate information sharing
for ship in self.humanity.ships:
ship.share_information("Quantum event detected!")
# Determine the impact of the quantum event
impact_result = self.quantum_event.impact(self.humanity)
print(impact_result)
```
9d6e056f No.3733887
>>3733725Reminds me of the Cern Demon Portal oh wait thats exactly what this situation is.
0fa7b1ba No.3733937
https://gizmodo.com/gizmodo-monday-puzzle-escape-the-basement-1851269645Puzzle #32: Forehead or Dead
A madman is holding you and nine strangers captive. He subjects you to a twisted mind game to earn your freedom. He has a stack of cards with the numbers 0 through 9 printed on them. He tapes a card to every person’s forehead so everyone can see everybody else’s card but not their own. Assigned numbers may repeat (e.g. eight people could get 7s while the other two get 0s or any other combination). After everyone has had time to observe everyone else’s numbers, your captor counts down and you all must shout a number at the same time. If at least one person guesses the correct number on their forehead, then you all go free. Otherwise you’ll be condemned to solve riddles in his basement forever.
As a madman with a passion for problem-solving, he allows the group to confer before he distributes the cards. Once cards are revealed no communication (including nonverbal) is allowed other than shouting a number on cue. The villain may listen in on the group strategy and adapt his choices accordingly! Devise a strategy that guarantees your freedom.
I recommend solving this for two or three people first and then trying to generalize the approach. Note that in the two person case, the cards only say 0 or 1, and in the three person version they say 0, 1, or 2.
I’ll be back next Monday with the solution. I hope it’s not too late for you.
8d7047e3 No.3733942
>>3733937>If at least one person guesses the correct number on their forehead, then you all go free>he allows the group to confer before he distributes the cardsThey agree, during the conference, to shout out the other persons numbers, so that then those people can shout out their own numbers.
b5b010d4 No.3733958
>>3733937another version of "prisoners dilemma"
beadcfa7 No.3734086
>>3733942It would take a bit of skill, since they have to shout the numbers at the same time.
But there are people who can do that. Actors often train to speak simultaneously by guessing from the first sound what the rest of the word will be.
c3010e3c No.3734093
>>3734086You can do it by simply looking at the person lips and see what sound they are ABOUT to make.
Four and Five or Six and Seven becomes a toss up, but with so many people, by chance, half will get it right.
d71b90b5 No.3734167
>>3733937Okay guys, this is how I'm gonna save all our asses (in this hypothetical scenario). So the trick is we all bet against each other. Each of us is assigned a number 0 - 9 and we each assume that the sum of all assigned cards will have a remainder corresponding to our number when divided by 10. Then when we see each other's cards, we each speak the number that when added to the sum of everyone else's cards gives the remainder of our assigned number mod 10.
So for instance, if my assigned number is 7 and I sum all the cards I see and get 45; then the remainder when divided by 10 is 5, so I should guess 2 is my card. Because 5 + 2 gives the remainder corresponding to my assigned number.
Because the remainder can only be 0 - 9 and everyone is guessing mutually exclusive scenarios, we can't all be wrong. So one of us must be right. This strategy is guaranteed to win, even if our mad captor eavesdrops on us.
dc777189 No.3734180
>>3734167You forget that assigned numbers can repeat. You don't know what the remainder will be, because you can't guess what the sum is.
a52e8b94 No.3734441
'Tis the Math Monday before Pi Day!
>>3734167 got last week's puzzle. The author said it was among the hardest of these Gizmodo puzzles yet, so impressive work! Now on to this week's puzzle.
https://gizmodo.com/gizmodo-monday-puzzle-pi-day-1851310995Puzzle #33: Pi Day
A string is tightly wrapped around Earth’s equator. You splice additional string in to add just enough slack so that you could (in principle) raise the new longer string exactly 1 foot off the ground all around the world. How much string did you add? How much would you need to add to a string wrapped around a basketball to raise it by 1 foot?
In the image below, which area is the largest, yellow, blue, or red? The squares are all the same size and all of the circles within the same square have equal size. The circles just barely kiss each other and the edges of the squares at single points.
c50a0ef7 No.3734459
>>37344411: 2*Pi for any sphere
[original = 2*Pi*R
new = 2*Pi *(R+1)
== 2*Pi + 2*Pi*R]
2: Yellow == blue == red,
[yellow = X
blue = X/2^2 * 4 == X
red = X/4^2 * 16 == X]
>>3734441 5ae7728f No.3734480
>>3734441set diameter of earth per quadrant as in four quadrants
to raise diameter by a foot, calculate each raise by inch of foot.
set to 12 diameters
Account for quadrants
12/4=3 figurative diameters
add these figurative diameters to the original raised diameter
12+3 =15 .then account for total figurative diameters of each figurative quadrant raised
15/4 = 12.75
15 -12.75 = 2.25 difference of figurative diameters
Add the difference to account for all figurative raised diameters/quadrants.
15+2.25=17.25
Then Add the figurative to the original raised diameter and average by foot.
12+17.25=29.25
29.25/12 for 2.4375 times total.
d71b90b5 No.3734522
>>3734459Thank goodness, someone finally beat me to the punch! This is correct. For the first puzzle, the answer is always 2pi times the radial increase, which in this case is 1 ft. Same for a baseball as for the entire Earth. For the second puzzle, the areas are all the same. It's obvious that the same
proportion of the square with a single circle is occupied by the circle as a quadrant of the square with 4 circles, which is the same proportion for the 1/4 by 1/4 corner of the square with 16 circles. All that changes is that the total square is broken up into smaller squares, each with the same proportion of circle to non-circle area. And because the 3 total squares are all the same size, the non-circle areas are all the same.
Happy early Pi Day!
f6e4e2ad No.3734985
Math Monday!
>>3734459 got both of last week's pi puzzles. Way to go! Now on to this week's challenge.
https://gizmodo.com/gizmodo-monday-puzzle-willy-wonka-scam-1851316654Puzzle #34: Fool’s Golden Ticket
Willy Wonka is selling new chocolate bars. They’re rectangular bars comprised of a 3x7 array of individually filled chocolate squares. Some squares are filled with fizzy lifting drink, while others have snozzberry filling. The arrangement of the flavors is randomly assigned from bar to bar.
Notice in the bar above that the four squares marked 1 form a rectangle whose corners are all snozzberry, whereas the squares marked 2 form a rectangle whose corners are all fizzy lifting drink (two-by-twos and three-by-threes are still rectangles). Wonka promises that anybody who buys a bar where NO four squares of the same type form a rectangle will win a visit to his factory. Your Uncle Joe starts emptying your life savings for chocolate, but you sense a scam. How can you convince Uncle Joe that Wonka’s winning bars don’t exist?
5ae7728f No.3735019
>>3734985Only a percentage of winnings bars, distributed over a percentage of total bars, distributed over a percentage of win per bar, distrubuted over a total amount of win in total, lowers the amount of win below 0.
a9795b0e No.3735048
>>3734985>Your Uncle Joe starts emptying your life savingsI have Uncle Joe arrested for theft of my money.
There are not enough colors to cover the squares. It is a scam. There is one square too many to cover with two colors.
93f6dad4 No.3735207
>>3735198No doubt it's a special purpose binary only known to caribou furries. :)
https://en.wikipedia.org/wiki/Gray_code d71b90b5 No.3735212
>>3734985There are only 6 (2^3 - 2) possible columns with both red and blue squares (excluding solid color columns). Consider you have only 6 columns (3x6 bar). Either all of the 6 possibilities for non-solid (color) columns are enumerated, in which case there is no rectangle. Or there is a repeat, in which case there must be a rectangle formed by the repeated columns. For the case of a 3x6 bar with no repeats, if you add an extra column (making it a 3x7 bar), you are guaranteed either a repeat or a solid column. A solid column can form rectangles with itself or the 3 possible columns with two squares of the solid column's color. Therefore, with a 3x7 bar it's impossible to not have a repeated column or a solid column and a column with two of the solid column's color, which ensures there must be a rectangle with squares of the same color for corners.
It's a scam, Uncle Joe!Tidbit: If it's known your bar has at least one solid color column, it only needs to be 3x4 to assure a rectangle is formed of the same color squares. Can you explain why?
d71b90b5 No.3735213
>>3735212Strike the 3x4 on the last part. Meant 3x5.
d129511c No.3735357
>>3735207Gray code changes only one digit at a time, so it's not that either.
eca85d4f No.3735364
>>3735357No, of course not. That's why the post said "No doubt it's a special purpose binary only known to caribou furries." Gray code is also known to non-caribou. Anyway, there are a few variants of Gray code.
ad261b00 No.3735645
Monday puzzle time, fuckers! Credit for solving last week's puzzle goes to
>>3735212. Super sleuths assemble to crack this week's murder mysteries!
https://gizmodo.com/gizmodo-monday-puzzle-sherlock-holmes-whodunit-1851350706Puzzle #35: Whodunits
1. It was a bright Tuesday afternoon, and Sherlock and Watson approached the apartment building as the coroners hauled away the body. The Chief of Police, Henry Meanswell, approached the men and said: “I know you boys love a crime scene, but I’m afraid your services won’t be needed here. This is an open-and-shut case of suicide.”
“Do you mind indulging us with what you know took place here today?” replied Sherlock.
Meanswell glanced at his watch and sighed. “A man named Diddy Jump was found dead on the front lawn of his apartment building. It appears he jumped out of the window of his studio apartment. His landlord, a sweet old lady named Agatha, found him. She explained to us that Diddy’s wife recently left him and he’s had trouble coping—drinking to excess and causing a ruckus in the building. Poor lady seems shaken up by the whole ordeal.”
“Did you inspect his apartment?”
“Yep, Agatha used her master key to let us in about 20 minutes ago, and it was like a pit of despair in there. Pitch black, beer bottles everywhere, and a stale stench. As soon as we flicked on the light, we saw the suicide note on the bed. It said that he couldn’t continue on his path of self-destruction and he wanted to end it all. Very sad, really.”
“Sad indeed, I suspect we have foul play on our hands.”
Why does Sherlock suspect a murder? ad261b00 No.3735646
>>37356452. [This one was inspired by a post on puzzling.stackexchange by user Puzzlees]
Sherlock didn’t flinch when he saw Mrs. Howe’s body dangling from her dining room rafters.
“This one’s gotta be a suicide,” pled Chief of Police, Henry Meanswell. “The only reason I haven’t already booked it is because of my mishap at last week’s crime scene. Sorry to call you here so late, but I figured I should let you take a look first.”
Sherlock inspected the noose around Mrs. Howe’s neck. “She’s wearing a wedding band. It’s always the husband.”
Meanswell had an eager retort, as though he had practiced: “That was my first thought too. In fact, her kids and neighbors report that they’ve had extreme marital trouble and Mr. Howe has been violent in the past. However, he has an airtight alibi.”
“Seldom such a thing,” smirked Sherlock.
“Mr. Howe works at an automotive factory an hour and a half drive away. Security footage and multiple eyewitnesses confirm he was at work all day and he clocked out at 5:30 pm. Our forensics team analyzed the rope burns around the victim’s neck and used new high quality instruments to verify that Mrs. Howe died by asphyxiation at exactly 6:00 pm. Even if her husband raced at top speeds, there’s no way he could have made it here in time. Unless you think he trapped her in a noose and set up some contraption to drop her while he was far away? Or maybe he hired a hitman?”
“He didn’t need a contraption nor a hitman. Bring Mr. Howe in for questioning.”
Why doesn’t Sherlock view Mr. Howe’s alibi as exonerating? 57e84fa9 No.3735700
>>3735645The room was pitch black but an open window on a sunny day would have left a bright lit room.
The window could not have been open and could not be closed after a jumper.
57e84fa9 No.3735702
>>3735646The factory and the Howe residence are in different time zones. Moving (assuming) east from Central to Eastern could lose an hour. That means Mr. Howe could arrive home at 6pm.
d71b90b5 No.3736142
>>3735645>>3735700>The room was pitch black but an open window on a sunny day would have left a bright lit room. The window could not have been open and could not be closed after a jumper.This. The stale air in the room also suggests the window was not opened. And the "suicide" note reads more like he was committing to sobriety, if it really is his handwriting.
>>3735646Mr. Howe could have met his wife somewhere between work and home and strangled her there. Then he drove her body home and strung her up. When Sherlock inspected the noose around her neck, maybe he noticed bruises inconsistent with a rope. Of course, Mr. Howe could have strangled her with a rope if the murder was premeditated.
2daacc69 No.3736534
Puzzle time, fools! Last week's first murder mystery was cracked by
>>3735700, and credit for wrecking Mr. Howe's alibi goes to
>>3736142. Clever deductions! Now prove you're not an April fool by solving this week's new puzzles.
https://gizmodo.com/gizmodo-monday-puzzle-april-fools-day-1851350730Puzzle #36: April Fools
1. A rope ladder hangs over the edge of a ship. The ladder is 20 feet long, and the rungs are each 1 foot apart. The bottom rung just barely grazes the water. The ocean tide rises 3 inches per hour. How much time will pass before the bottom nine rungs of the ladder are submerged under water?
2. What’s worth more, a gallon of nickels or half a gallon of dimes?
3. A man leaves home and takes three left turns. When he arrives back at home he sees two men wearing masks. Who are these men?
4. You meet two girls named Chloe Smith and Zoe Smith. They look alike and you ask if they’re twins. They say “No, but we have the same parents and we were born on the same day of the same month of the same year.” How is this possible?
5. I feel bad only leaving you with gimmicky puzzles so I’ve included one real one. I come to you with a curious observation. I pick a number and if it’s even, I divide it by 2 but if it’s odd, I multiply it by 3 and then add 1. I then repeat this process on whatever the resulting number is. For example, if I start with 5 then the sequence goes: 5, 16, 8, 4, 2, 1. This is because 5 is odd, so I start by multiplying by 3 and adding 1 to get 16, which is even, so I divide by 2 to get 8, which is also even, and so on. I’ve noticed that no matter what number I start with, I always get to 1 eventually.
Can you explain why? This one shouldn’t be too hard, but if you need a hint I’ve supplied one here.
4a0d7f6a No.3736535
>>37365341, It wont. Boats float, ya dingus.
2, Dimes are physically smaller, but worth twice that of nickles. Even though the allowed volume is halved, the dimes would be worth more.
3, The umpire and the catcher.
4, I dunno, IVF maybe.
5, You're guaranteed to make an even number at least every other step. Sometimes multiple. Anyways,
https://en.wikipedia.org/wiki/Collatz_conjecture 619fe088 No.3736576
>>3736534>>3736535I will echo these answers except for #4.
4. They could be lying or instead of twins, they are something else like triplets, quads, quints - you know, like littermates.
74866296 No.3736625
>>3736537
> how'd you get red bold?
Red text works differently than bold text. It must be the first text on a line.
Two equal signs at the beginning of a line and two equal signs at the end makes it red.
aa87e9dc No.3736655
>>3736653
Yeah, a couple.
aa87e9dc No.3736661
>>3736660
Two asterisks in front and two more at the end spoiler text.
a6439f88 No.3736667
>>3736659
Now try it without bolding. :3
aa87e9dc No.3736673
>>3736667He just copying "nigger" from the previous post.
f6f57eb8 No.3737114
Monday puzzle time!
>>3736535 and
>>3736576 got last week's puzzles. No fooling you! Now for the new puzzle.
https://gizmodo.com/gizmodo-monday-puzzle-perfect-poker-hand-1851383278Puzzle #37: Transparent Poker
You and I will play a variant of poker. We will spread out the entire deck of 52 cards face up. You will pick any five cards you want, and then I will pick any five cards I want from the remaining deck. Then you have a chance to discard any number of cards you want from your hand (including discarding no cards), place them permanently out of the game, and replace them with any cards of your choice from the remaining deck. I then get to do the same. Whoever has the best five-card poker hand after the replacements wins.
What cards should you pick on your first turn to guarantee that you win the game? If we end with the same hand, then I win.
The puzzle has more than one solution, but one stands out as the most natural. As a bonus,
what is the worst five-card poker hand that you can start with to still guarantee a win? Find the ranking of poker hands here* if you need a refresher.
*
https://en.wikipedia.org/wiki/List_of_poker_hands d71b90b5 No.3737342
>>3737114Reckon the best hand to pick on the first turn is
four 10s and a king. But the king can be any other card really. This should guarantee a win with at worst a 10-high straight flush. And I suppose the worst poker hand to guarantee a win is
a jack and a 6 of the same suit and the three 10s of the other suits.
>>3736776>>3736784Nice.
b3bb47de No.3737669
Happy Tax Evasion Day! Just kidding. We all need to contribute our fair share to keep society running. Anyway,
>>3737342 got last week's puzzles. Now on to this week's new puzzle.
https://gizmodo.com/gizmodo-monday-puzzle-tax-evasion-1851405379Puzzle #38: Tax EvasionYou and a Tax Collector sit across a table with 12 paychecks on it. The paychecks are worth every whole dollar amount between 1 and 12 ($1, $2, $3, …, $12). You select paychecks for yourself one at a time, but every time you take a paycheck, the Tax Collector immediately takes all remaining checks whose values are factors of the number you chose. For example, if you choose the $8 check, then the Tax Collector will take the $1, $2, and $4 checks because 1, 2, and 4 are factors of 8. If the $2 check had already been claimed on a prior turn, then the Tax Collector would only take the $1 and $4 checks.
The Tax Collector must be able to take some paycheck on every turn. If you run out of legal moves (for example, if only paychecks $8 and $9 remain, then you can’t take either of them because their factors aren’t available to your opponent) then the Tax Collector takes all remaining paychecks.
What is the largest amount of money you can claim for yourself in this game? 75ca45e8 No.3737695
>>3737669Me Tax
11 1
9 3
8 2,4
10 5
12 6
7
5d53053b No.3737799
https://www.youtube.com/shorts/eYrFJI2DzT8?feature=shareThat is 86,400 cents a day,
That is $864 dollars a day,
That is $6,048 dollars a week,
That is $25,920 dollars a month,
That is $311,040 dollars a year.
4aae236d No.3737995
>>3737860Eat the rich!
Only government should have wealth. Everyone else needs to be poor. True equality.
4a685aa0 No.3737996
>>3737990Wasn't expecting Nick to join in, that's wild. 😹
I didn't think much of this meme at first, but it's slowly grown on me ever since this one (and a few others) got me into Out of Placers.
dde23a54 No.3738299
Math Puzzle Monday! Congrats to
>>3737860 for adroitly dealing with the taxman. Now for this week's new challenge.
https://gizmodo.com/gizmodo-monday-puzzle-number-that-describes-itself-1851383295Puzzle #39: A Self-Referential NumberOnly one 10-digit number has the following property. Its left-most digit is the number of 0s in the number, the next digit is the number of 1s in the number, the next is the number of 2s, and so on until the right-most digit, which is the number of 9s in the number.
Find the number. Numbers can’t begin with a zero.
An example of a four-digit number with this property is 2020. The first digit indicates that the number contains two 0s, the next indicates zero 1s, the next indicates two 2s, and the final indicates zero 3s.
Bonus: you can seed the look-and-say sequence with any whole number. For example, if you started with 39, then the next entry would be 1319 (one three, one nine). Conway proved that all seeds yield a sequence whose entries grow to infinity, with only one exception.
Find the exception. df1f0316 No.3738895
Monday puzzler! Last week's challenges were solved by
>>3738309. Now on to this week's new challenges.
https://gizmodo.com/gizmodo-monday-puzzle-1-percent-club-1851428073Puzzle #40: 1% QuestionsBonus challenge: Players on the show only get 30 seconds to solve each puzzle, so pull out a stopwatch if you want to simulate the real experience. I expect most people will need more time than that.
Question 1: In the following sequence, what do the letters V and C stand for?
V C C C V C C C V C C C C C V C C C C C V C C C C C
Question 2: On a digital 24-hour clock (military time) that displays hours, minutes, and seconds, how many times in each 24-hour period do all six digits change simultaneously?
Question 3:Jamaica + Japan = 124
Argentina + Armenia = 1245
France + Brazil = 23
England + Germany = ?
