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Tax Collector (Posted on 2015-05-26) Difficulty: 2 of 5
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.

See The Solution Submitted by Ady TZIDON    
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Solution Comment 6 of 6 |
(In reply to Answer / no solution by Jer)

The link I posted previously has a link to an analysis by Dan Hoey:
https://oeis.org/A019312/a019312.txt
In which he gives the order of numbers to choose for n up to 158.
a(48)=734: 47,25,35,21,39,33,27,45,26,46,38,34,18,42,30,28,44,40,36,32,48

  Posted by Jer on 2015-06-02 09:15:39
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