Problems built purely to be interesting.
9 topics · 9 curated works
No prior grounding assumed.
Mathematical Recreations and Essays
W. W. Rouse Ball · 1892
Treats puzzles, paradoxes and games as a single subject on the grounds that solving any of them is a small piece of genuine mathematical research,…
+3 more at this level
Assumes you know the vocabulary.
A Budget of Paradoxes
Augustus De Morgan · 1872
A running catalogue of circle-squarers, angle-trisectors and other self-published mathematical cranks the author corresponded with, arguing their…
+2 more at this level
Primary sources and full treatments.
Solving the Rubik's Cube Without Human Knowledge
Stephen McAleer, Forest Agostinelli, Alexander Shmakov & Pierre Baldi · 2018
An algorithm given no human solving method teaches itself to solve any scrambled cube by working backwards from the solved state, matching solution…
+1 more at this level
9 works
W. W. Rouse Ball
Treats puzzles, paradoxes and games as a single subject on the grounds that solving any of them is a small piece of genuine mathematical research, not entertainment adjacent to it.
link checked 17 Sept 2026Sam Loyd
A posthumous compilation of puzzles Loyd created for newspapers and exhibitions, arguing a puzzle's value is the single moment of insight that makes its trick look obvious in hindsight.
link failing as of 17 Sept 2026Henry Ernest Dudeney
Argues the value of a puzzle is in the general method needed to crack it, and groups hundreds of problems by the reasoning technique they teach rather than by subject.
about 11 hours to readlink checked 17 Sept 2026Edward de Bono
Argues creative problem-solving is a learnable technique distinct from step-by-step logic, because it works by deliberately restructuring how a problem is framed rather than searching harder within one framework.
Augustus De Morgan
A running catalogue of circle-squarers, angle-trisectors and other self-published mathematical cranks the author corresponded with, arguing their errors are instructive because each fails in exactly the way ordinary reasoning invites.
link checked 17 Sept 2026Henry Ernest Dudeney
Frames each puzzle inside a fictional narrative, arguing a good puzzle is a designed object with a fair, discoverable solution rather than a trick question.
about 4 hours to readlink checked 17 Sept 2026Agnes M. Herzberg & M. Ram Murty
Shows a completed Sudoku grid is equivalent to a proper colouring of a specific graph with chromatic number nine, turning the puzzle's structure into a question about graph theory and Latin squares rather than trial and error.
link checked 17 Sept 2026Stephen McAleer, Forest Agostinelli, Alexander Shmakov & Pierre Baldi
An algorithm given no human solving method teaches itself to solve any scrambled cube by working backwards from the solved state, matching solution lengths that hand-coded solvers only reach using human-derived rules.
link checked 17 Sept 2026Josh Rozner, Christopher Potts & Kyle Mahowald
Argues a cryptic clue is a genuine test of language understanding because a literal definition and an independent wordplay derivation must both resolve to the same answer, and shows current NLP models fall far short of expert human solvers on it.
link checked 17 Sept 2026