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 Tax Collector (Posted on 2015-05-26)
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 No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 re(3): Thoughts. | Comment 4 of 6 |
(In reply to re(2): Thoughts. by broll)

I just want to point out although the maximum may be 50 = 8+9+10+11+12, there are many orders to get there.

The only things that matter are:
the 11 must be chosen first,
the 8 must be chosen before the 12,
the 9 must be chosen before the 12.

(I count 8 orders.)

 Posted by Jer on 2015-05-26 09:39:58

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