# board games

Published articles for board games.

This is one page of public article previews, not the complete archive. Follow Next page to continue. Summaries are not the original full articles.

## 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 $\{ 1, 3, 4, 5 \}$.

## A Rook Game

DevFeed: [A Rook Game](<https://devfeed.tech/articles/a-rook-game-40365.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2014/08/31/a-rook-game/>)

Published: 2014-08-31T17:51:37Z

Content type: tutorial

Language: en

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

Topics: [Algorithm](<https://devfeed.tech/topics/algorithm.md>), [Mathematics](<https://devfeed.tech/topics/mathematics.md>)

Tags: [algorithm](<https://devfeed.tech/tags/algorithm.md>), [board-games](<https://devfeed.tech/tags/board-games.md>), [chessboard](<https://devfeed.tech/tags/chessboard.md>), [game](<https://devfeed.tech/tags/game.md>), [games](<https://devfeed.tech/tags/games.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [strategy](<https://devfeed.tech/tags/strategy.md>), [symmetry](<https://devfeed.tech/tags/symmetry.md>)

### AI overview

This article presents a rook game on an 8x8 chessboard in which players move only south or west. It shows that symmetry provides the optimal strategy: move the rook to the diagonal whenever possible and return it there after the opponent moves it away. The first player wins from an off-diagonal starting square; otherwise, the second player wins.

### Source excerpt

Problem: Two players take turns moving a rook on an 8x8 chessboard. The rook is only allowed to move south or west (but not both in a single turn), and may move any number of squares in the chosen direction on a turn. The loser is the player who first cannot move the rook. What is the optimal play for any starting position? rook-board Solution: Take advantage of the symmetry of the board.

## How theoretical computer science explains the complexity of puzzle games

DevFeed: [How theoretical computer science explains the complexity of puzzle games](<https://devfeed.tech/articles/want-to-make-a-great-puzzle-game-get-inspired-by-theoretical-computer-science-40351.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2014/03/17/want-to-make-a-great-puzzle-game-get-inspired-by-theoretical-computer-science/>)

Published: 2014-03-17T10:00:55Z

Content type: opinion

Language: en

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

Topics: [computational complexity](<https://devfeed.tech/topics/computational-complexity.md>), [Algorithms, Complexity](<https://devfeed.tech/topics/algorithms-complexity.md>), [Computer science](<https://devfeed.tech/topics/computer-science.md>), [Algorithms](<https://devfeed.tech/topics/algorithms.md>), [Mazes](<https://devfeed.tech/topics/maze.md>)

Tags: [algorithm](<https://devfeed.tech/tags/algorithm.md>), [art-gallery-problem](<https://devfeed.tech/tags/art-gallery-problem.md>), [bin-packing](<https://devfeed.tech/tags/bin-packing.md>), [board-games](<https://devfeed.tech/tags/board-games.md>), [computational-complexity](<https://devfeed.tech/tags/computational-complexity.md>), [computer](<https://devfeed.tech/tags/computer.md>), [computer-science](<https://devfeed.tech/tags/computer-science.md>), [exp](<https://devfeed.tech/tags/exp.md>), [game](<https://devfeed.tech/tags/game.md>), [games](<https://devfeed.tech/tags/games.md>), [games-on-graphs](<https://devfeed.tech/tags/games-on-graphs.md>), [graph-coloring](<https://devfeed.tech/tags/graph-coloring.md>), [greedy-spiders](<https://devfeed.tech/tags/greedy-spiders.md>), [mario](<https://devfeed.tech/tags/mario.md>), [nintendo](<https://devfeed.tech/tags/nintendo.md>), [np](<https://devfeed.tech/tags/np.md>), [np-completeness](<https://devfeed.tech/tags/np-completeness.md>), [np-hard](<https://devfeed.tech/tags/np-hard.md>), [pancake-flipping](<https://devfeed.tech/tags/pancake-flipping.md>), [pspace](<https://devfeed.tech/tags/pspace.md>), [puzzle](<https://devfeed.tech/tags/puzzle.md>), [science](<https://devfeed.tech/tags/science.md>), [starcraft](<https://devfeed.tech/tags/starcraft.md>), [video-games](<https://devfeed.tech/tags/video-games.md>)

### AI overview

The article explains that NP-hardness in games describes worst-case computational complexity, not how difficult a game is for human players. It uses examples including Pokémon, Super Mario Bros., Candy Crush Saga, Pac-Man, Doom, Starcraft, Tetris, chess, checkers, and Go to discuss hardness results and practical algorithms.

### Source excerpt

Two years ago, Erik Demaine and three other researchers published a fun paper to the arXiv proving that most incarnations of classic nintendo games are NP-hard. This includes almost every Super Mario Brothers, Donkey Kong, and Pokemon title. Back then I wrote a blog post summarizing the technical aspects of their work, and even gave a talk on it to a room full of curious undergraduate math majors. But while bad tech-writers tend to interpret NP-hard as "really really hard," the truth is more complicated.