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?