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Nine Linked Rings (Baguenaudier) (1872) — The Year an Origin-Unknown Ring Puzzle Turned Out to Use Binary Math 81 Years Before a Telegraph Engineer Patented the Same Idea
Nine Linked Rings, or Baguenaudier: remove rings from a bar one at a time until the last one slides free. Its origin is said to be China, but nothing is settled; the earliest confirmed records are a 16th-century Chinese text and, around the same time, the writings of Italian mathematician Luca Pacioli. In 1872, Lyon mathematics enthusiast Louis Gros became the first to theorize the puzzle's solution as a binary table. The same idea was independently reinvented 81 years later, in 1953, when telegraph engineer Frank Gray patented what communications engineers now call the "Gray code." As a physical puzzle, a 1970 patent by William Keister became "Spin-Out," an early product of Binary Arts (founded 1985, now ThinkFun), still sold today. This piece follows the 150-year lineage of a single ring mechanism.
The Seven Bridges of Königsberg (1736) — The Year Euler Erased the Map to Solve a Sunday Puzzle
The answer is simple. In 1736, the mathematician Leonhard Euler proved that no walk existed that crossed all seven bridges of the Prussian town of Königsberg exactly once and returned to its start. The town's four landmasses were connected by 5, 3, 3, and 3 bridges respectively — all odd numbers. His paper, "Solutio problematis ad geometriam situs pertinentis," was presented on August 26, 1735, and published in 1741. By reducing landmasses to points and bridges to lines, Euler founded what became graph theory — the same logic taught in schools today as the rule for "one-stroke" drawing puzzles. This article traces how that 290-year-old proof still shapes the design of today's routing puzzle games, from Cosmic Express to Lyne to Mini Metro.
Peg Solitaire (1697) — The Day a Game With No Inventor Became the Math of Proving "Unsolvable"
On a cross-shaped board of pegs, you jump one peg over its neighbor and remove it, again and again, hoping to end with a single peg left. The earliest record of Peg Solitaire appears in 1697, in the French court periodical Mercure Galant under Louis XIV. No inventor is known. The popular legend that a prisoner in the Bastille devised it traces back no further than an English book from 1801, and puzzle historian John Beasley calls it unsupported by any earlier French source. In 1912 Ernest Bergholt found an 18-move solution to the classic problem; in 1982 Winning Ways for Your Mathematical Plays introduced the "pagoda function," a tool for proving certain positions mathematically unreachable. In 2007 the board resurfaced as puzzles inside Professor Layton and the Diabolical Box. This piece traces a single ruleset that has been played for over three centuries without ever needing a named inventor.
五格骨牌（1965）——Solomon W. Golomb 命名的五方块图形，如何演变为 Tetris
1965年，美国数学家 Solomon W. Golomb 在其著作《Polyominoes》中，将由五个正方形连接而成的十二种图形「五格骨牌（pentomino）」的理论整理成书。这一命名可追溯到1953年哈佛大学的一次演讲，1957年经由 Martin Gardner 的专栏传到普通读者手中，1975年又发行了俄语译本。到了1984年，莫斯科的青年 Alexey Pajitnov 凭借童年时对五格骨牌的记忆，在一台实验用计算机上移动图形，Tetris 由此诞生。本文追溯这一五方块图形耗时三十余年环游世界的历程。
Henry Dudeney (1907) — Four Hinged Pieces That Turn a Triangle Into a Square
In 1907, English puzzle maker Henry Dudeney published, within The Canterbury Puzzles, the Haberdasher's Puzzle: cutting an equilateral triangle into just four pieces that reform into a square. Hinged together, the pieces could transform with a single fold, and the dissection drew attention in its day -- yet the proof that four pieces were truly minimal remained unresolved for a surprisingly long time, settled only by a 2024 computational-geometry paper. Tracing Dudeney's rivalry with Sam Loyd and his rediscovery through Martin Gardner, this piece rereads how a paper puzzle took 117 years to reach computer science.
河内塔（1883）—— 留下递归遗产、永无终结的64枚圆盘
1883年，法国数学家Édouard Lucas以「N. Claus (de Siam)」为笔名推出了一款木制玩具。三根柱子，大小各异的圆盘，仅有两条规则。然而其朴素外表之下，蕴含着移动n枚圆盘至少需要2ⁿ−1步的递归数学。本文从历史视角重新审视这款玩具的真正起源、贝纳勒斯关于64枚圆盘完成时世界将终结的虚构传说，以及「递归」与「状态空间」的思想为后世计算机科学与现代谜题所留下的遗产。
魔方（1974）——43京种配置的迷宫，与唯一一个解
1974年，布达佩斯的建筑师厄尔诺·鲁比克为教学目的削出了一个小小的立方体，这个物体最终将拥有43京种配置、唯一一个完成形的"状态空间"握于掌心。本文通过一次和二次文献，追溯这一玩具的确切出处——1974年的发明、1980年的全球登场，以及2010年证明的"神之数=20"——并作为历史重新解读：这个没有显示屏、没有电源的物体，是如何在半世纪前便以实物体现了现代解谜设计者口中的"可逆性""唯一解""待探索的空间"等语汇的。
15数字推盘（1880） — 萨姆·劳埃德骗倒世界的那一步无解棋局
1880年初，「15数字推盘」的狂潮席卷美国与欧洲。然而被世人奉为发明者的萨姆·劳埃德，实为在狂潮消退十六年后才冒领功劳的冒充者。本文追溯这个木盒的真实来源，以及劳埃德以悬赏为名的「14与15对调的盘面」在数学上绝对无解的1879年证明，并从历史角度重读滑块拼图留给现代数字谜题设计的遗产：「可解性的保证」。
