The Dollar Game – Numberphile



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With Dr Holly Krieger from Murray Edwards College, University of Cambridge.

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33 thoughts on “The Dollar Game – Numberphile

  1. So sum of money < 0, definitely not winnable and sum of money >= genus definitely winnable. Would be interesting to see how the difficulty scales in that middle range.

  2. In the 3 vertices, 3 edges (triangle) the genus is 1. There's a trivial solution where all vertices are 0. You have already won. This will also be the case for all genus > 0 where all vertices contain 0 or > 0 dollars.

  3. However I understand economics and I just fill up the vertices with dollars from the central bank, which has an infinite supply.

  4. In that "bad game" example im gonna donate from zero, zero is now -2, 1 is now 2 and -1 is now 0. Now Im gonna donate money from 2 which is 1 before two times in a row and now -2 is 0, 0 is now 1 and 2 is now 0. I've won the game.

  5. >there has to be enough money on the board to get everyone out of debt
    obviously a maths game and not an economics game

  6. This reminds me of using the Critical Path Method to solving a flow issue between various processes in manufacturing, etc. Usually the CPM is used in relationship to time.

  7. Can you make a winnable game not winnable with bad moves? I think the answer is yes, but I doubt that's provable mathematically.

  8. in the first game, couldn’t you just make the guy with 2 give money to the two guys in debt and be done in two turns

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