The subset sum puzzle
A mathematical puzzle game is presented where one player chooses 10 numbers from 1-100, and the other must find two distinct subsets with equal sums. The challenge is to determine which player has a winning strategy.
Summary
The video introduces a competitive mathematical puzzle involving subset sums. The game mechanics are straightforward: one player selects 10 numbers from the range 1-100, while the opponent must identify two different subsets of those numbers that produce identical sums. An example is provided showing two pairs of numbers that both sum to 102, demonstrating a winning scenario for the subset-finder. The puzzle's core question revolves around game theory - whether the number-chooser can always select a collection of 10 numbers that prevents any two subsets from having matching sums, or if the subset-finder can always guarantee finding such a pair regardless of the initial selection. This is presented as part of an ongoing monthly puzzle series created in collaboration with MoMath (Museum of Mathematics), with the solution to be revealed to subscribers at a later date.
About this episode
Part of a series of monthly puzzlers. Stay subscribed to see the solution
Key Insights
- The presenter demonstrates that finding two subsets with equal sums is possible by showing two different pairs of numbers that both add up to 102
- The core puzzle question asks which player has a winning strategy - whether the number chooser can always prevent equal subset sums or the challenger can always find them
- This mathematical puzzle is part of a monthly series created in collaboration with MoMath (Museum of Mathematics)
Topics
Transcript
[0:00] You and I are going to play a game. The way it works is that I look at all of the numbers from one up to 100 and I choose 10 of them. I then present you with these 10 numbers and your challenge is to find two distinct subsets from whatever I choose that have the same sum. So, for example, in this case, these two different pairs of numbers each add up to 102. If you can do this, you win the game. But if I can find some collection of 10 numbers where no matter how hard you try, you can't find two [0:30] subsets that have the same sum, then I would win the game.…
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