December 07, 2008
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
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.
Hm, I'm pretty sure 124 is optimal!
I got 2957 v 2093 using the "greedy" algorithm. I a fairly certain it isn't optimal.
what's the highest possible score for Taxman 24?
Im pretty sure the Highest possible score in Taxman is something like 1227. Thats the highest I've gotten with my friends soo... Yah...
isn't that..... impossible?
I just got Score: 3006 Taxman: 2044
124 must be optimal. 19 is the correct first move as it is the largest prime on the board. Since 11, 13, and 17 are also prime and larger than half of 20, we cannot choose those, so the taxman gets them always. After the first move, there are 15 numbers that we can choose from left on the board, as 1, 11, 13, 17, and 19 are now gone. Since the taxman must receive at least one number each time we choose a number, the greatest number of picks that we have left is the floor of 15/2, which is 7. Thus we want 19 and the highest remaining 7 numbers, excluding 11, 13, and 17. The highest 7 remaining numbers would be, in descending order, 20, 18, 16, 15, 14, 12, 10. 19+20+18+16+15+14+12+10=124. Since there is a sequence of choices that will actually give us this outcome, that score is optimal.
Did you know that you can type in 999 and it will make a board with 999 numbers. You can get scores over 25000
Impossible to win on 3 board.
Yeah, 999 is hard. And yes, I knew that.
easy to beat 2 taxman hard on 500
First move should always be the largest prime number on the board.
Check here for scores taxman games up to n=50.
The lowest number you can win at is 4
Hey guys I'm doing this for my assignment at uni. I'd done the greedy method and according to my mate, it's optimal. Basically taking the largest number each time with the smallest divisor (there's always a number with at 1 divisor). This display really helped me out as I slowly developed and tested this with this board.
For 100, I got 2970 - 2080
For 24, I got 178 - 122
For 947, I got 275607 - 173271
Mind telling me how you did it Mr.28403?
3 is a tie and actually the smallest number you can win with is 2.