In 30 seconds
3Blue1Brown and MoMath pose a game about equal subset sums and ask which player can guarantee a win.
- 1The player’s taskFind two different subsets with the same sum.
- 2The chooser’s taskFind ten numbers with no equal-sum pair of distinct subsets.
- 3An open challengeThe short video leaves the solution for a later installment.
Takeaways
- Ten distinct integers are chosen from 1 through 100.
- One player seeks two distinct subsets with equal sums; the other seeks a selection that makes that impossible.
- The short video poses the puzzle without presenting the solution.
Read the edited text by chapter
The rules
Choose ten numbers and compare sums of subsets.
Imagine a game played with the integers from 1 through 100. I choose ten distinct numbers and show them to you.
Your task is to find two distinct subsets of those ten numbers whose sums are equal. For example, two different pairs might both add up to 102. If you find such a pair of subsets, you win.
Who can force a win?
Decide whether the chooser can prevent an equal-sum pair.
I win if I can choose ten numbers for which no two different subsets have the same sum. The puzzle is to determine which player has a winning strategy.
This is a monthly puzzler made with MoMath. The short video poses the question and leaves the solution for a later installment.
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