December 07, 2008

Taxman Game

Another gem from my neighbor Tom Sander. The "taxman" game is (apparently) an old programming exercise. But it is also a good game for practicing factors. I have been playing it a bit with Anthony (by hand). Here is a gadget that applies the rules of the game for you.

The rules are simple and fifth-grade friendly:

  • When you take a number, the taxman gets all the remaining factors.
  • You are only allowed moves that give the taxman at least one new number.
  • When you can't move any more, the taxman gets the rest.

It is worth playing without reading anything else - it is not too hard to find a heuristic that beats the taxman. The game was written up in an article by Moniot in the Feb 2007 MAA Horizons - an optimal strategy is not known.

I've gotten up to 121 points on the 20-size board; I am pretty sure this is not optimal. Can you beat the board with 100 squares? What is the best score you can get?

Posted by David at December 7, 2008 05:12 PM
Comments

David --

Highest I've been able to get to with board of 20 is 124 from drawing numbers in this order (19,14,10,20,16,15,12,18).

I suspect this is not optimal.

Best.

Tom

Posted by: Tom Sander at December 9, 2008 08:26 AM

Hm, I'm pretty sure 124 is optimal!

Posted by: David at December 11, 2008 09:22 PM

I got 2957 v 2093 using the "greedy" algorithm. I a fairly certain it isn't optimal.

John

Posted by: John Kemeny at January 5, 2009 04:09 PM

what's the highest possible score for Taxman 24?

Posted by: dude wheres my car? at November 4, 2009 06:57 PM

Im pretty sure the Highest possible score in Taxman is something like 1227. Thats the highest I've gotten with my friends soo... Yah...

Posted by: Dude What's mine say? at November 4, 2009 07:01 PM

isn't that..... impossible?

Posted by: dude wheres my car? at November 4, 2009 07:03 PM

hi

Posted by: at April 22, 2010 01:41 PM

I just got Score: 3006 Taxman: 2044

Posted by: dustin at July 13, 2010 05:46 PM
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