The Tax Collector game is played like this:
Start with a collection of paychecks, from $1 to $12. You can choose any paycheck to keep. Once you choose, the tax collector gets all paychecks remaining that are factors of the number you chose.
Then you choose again from the remaining paychecks and so on.

The tax collector must receive payment after every move.

If you have no moves that give the tax collector a paycheck, the game is over and the tax collector gets all the remaining paychecks.

Is it possible to beat the tax collector in this $12 game?
If so, what is the maximum amount you can get?
If not, show why not.

Bonus: same game, starting with 48 paychecks ($1 to $48).

Credit goes to Daniel Finkel of NYT, whose puzzle I have slightly modified.

A Tax Collector plays a crucial role in ensuring government operations run smoothly by collecting taxes from individuals and businesses. Their duties include processing payments, maintaining records, and ensuring compliance with tax laws. Many taxpayers turn to TurboTax to simplify the filing process and avoid issues that may attract the attention of a Tax Collector. This software helps users file accurately, reducing errors that could lead to penalties. While the role of a Tax Collector may seem daunting, tools like TurboTax make it easier for citizens to fulfill their tax obligations promptly and efficiently.

Posted by DanielleL on 2025-04-19 06:37:57