# Socks, a matching game based on an additive combinatorics problem

DevFeed: [Socks, a matching game based on an additive combinatorics problem](<https://devfeed.tech/articles/socks-a-matching-game-based-on-an-additive-combinatorics-problem-40478.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2023/10/14/socks-a-matching-game-based-on-an-additive-combinatorics-problem/>)

Published: 2023-10-14T06:00:00Z

Content type: article

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [math](<https://devfeed.tech/topics/math.md>), [structure](<https://devfeed.tech/topics/structure.md>)

Tags: [additive-combinatorics](<https://devfeed.tech/tags/additive-combinatorics.md>), [board-games](<https://devfeed.tech/tags/board-games.md>), [card-game](<https://devfeed.tech/tags/card-game.md>), [combinatorics](<https://devfeed.tech/tags/combinatorics.md>), [game](<https://devfeed.tech/tags/game.md>), [games](<https://devfeed.tech/tags/games.md>), [group-theory](<https://devfeed.tech/tags/group-theory.md>), [math](<https://devfeed.tech/tags/math.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [structure](<https://devfeed.tech/tags/structure.md>), [xor](<https://devfeed.tech/tags/xor.md>)

## AI overview

This article introduces Socks, a matching game modeled using six-dimensional binary vectors and additive combinatorics. It proves that any seven cards contain a valid zero-summing set, while six specific cards can avoid one, so the minimum guarantee is seven cards.

## Source excerpt

Can you find a set of cards among these six, such that the socks on the chosen cards can be grouped into matching pairs? (Duplicate pairs of the same sock are OK) Spoilers: If the cards are indexed as 1 2 3 4 5 6 Then the following three subsets work: $\{ 1, 2, 4, 5, 6 \}$, $\{ 2, 3, 6 \}$, and $\{ 1, 3, 4, 5 \}$.