The subset sum puzzle

2026-03-25 · Source: 3Blue1Brown · Field: Science & Research — Mathematics & Computational Sciences · Depth: Fundamental Awareness, quick

Summary

The "subset sum puzzle" describes a game where one player selects 10 distinct numbers from the integers 1 through 100. The second player's challenge is to identify two different subsets from these 10 chosen numbers that yield an identical sum. For instance, if the chosen numbers include elements that form two distinct pairs, each summing to 102, the second player wins. The central question posed by the puzzle is to determine which player possesses the winning strategy: the one who chooses the initial 10 numbers, or the one tasked with finding the equal-sum subsets. This puzzle is presented as part of a monthly series in collaboration with MoMath.

Key takeaway

For mathematicians or computer scientists exploring combinatorial problems, this subset sum puzzle highlights the inherent challenges in proving or disproving the existence of specific substructures within a given set. If you are designing algorithms for subset sum variations, consider the implications of such existence proofs, as they can inform the feasibility and complexity of search strategies. Engage with the puzzle to sharpen your intuition on combinatorial guarantees.

Key insights

The puzzle challenges players to determine if two distinct subsets with identical sums can always be found within 10 numbers chosen from 1 to 100.

Topics

• Subset Sum Problem
• Combinatorics
• Mathematical Puzzles
• Game Theory
• Number Theory

Best for: General Interest

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Editorial summary, takeaway, and curation by AIssential. Original article published by 3Blue1Brown.