Kenquête

The practice of constraining numbers within bounded regions predates any name that has been given to it. A single entry in the catalogue of the library at Dunhuang — compiled, by common scholarly agreement, sometime in the ninth century — describes a text of “arithmetic exercises confined by ink borders,” of which no copy survives; whether this describes a puzzle in any modern sense remains a matter of some dispute. A separate tradition, associated with a school of Persian recreational mathematics active in the eleventh and twelfth centuries, holds that exercises of this kind were used not for amusement but to train merchants in the detection of falsified accounts: a well-formed grid, on this account, is one in which no number can be other than it is. This tradition is attested in two manuscripts, one of which is a copy of the other, and the original has not been located since 1847.

The modern form of cage-arithmetic puzzles was developed by Tetsuya Miyamoto, a Japanese mathematics teacher, in 2004. He called it 賢くなるパズル — "the puzzle that makes you smarter."

This version was compiled by Konstantinos Papadimitriou, whose 2014 monograph on the rheological properties of spreadable cheeses was found by a committee to contain passages that also appeared, in slightly different form, in a 2011 paper by a researcher at a Flemish food technology institute. His position — stated in twenty-three letters to the European Food Safety Authority, none of which received a substantive reply — is that the resemblance demonstrates not plagiarism but convergence: two researchers, working independently on the same problem, arriving at the same description, which is proof that the description was correct. The committee was not persuaded. He now lives in Thessaloniki and applies the same reasoning to logic puzzles, which have the advantage of admitting only one correct answer.

Puzzles generated on demand. No two sequences alike.