Coin Weighing — credits and provenance ====================================== WHAT THIS IS ------------ An independent reimplementation of the counterfeit-coin balance puzzle, written from the published statement of the problem. No code, art, text or data was taken from any other implementation. The underlying puzzle is a piece of recreational mathematics in the public domain; nobody owns it, and this app claims no rights over it. THE ORIGINAL ------------ The twelve-coin version appeared in print as early as 1945: Howard D. Grossman, "The twelve-coin problem", Scripta Mathematica 11 (3-4), September-December 1945, pages 360-361. [DOCUMENTED] Richard Guy and Richard Nowakowski, "Coin-Weighing Problems", The American Mathematical Monthly 102 (2), February 1995, pages 164-167, doi 10.1080/00029890.1995.11990553, who record that the puzzle "was popular on both sides of the Atlantic during WW2; it was even suggested that it be dropped over Germany in an attempt to sabotage their war effort". [DOCUMENTED] C. A. B. Smith, "The Counterfeit Coin Problem", The Mathematical Gazette 31 (293), February 1947, pages 31-39, doi 10.2307/3608991 — the source of the table of maxima that this app's search is checked against. [QUALIFIED] Freeman J. Dyson, "1931. The Problem of the Pennies", The Mathematical Gazette 30 (291), 1946, pages 231-234, doi 10.2307/3611225. [QUALIFIED] QUALIFIED means the citation is real and quoted as published, but the paper itself was not retrieved: the 1946 and 1947 Mathematical Gazette are behind JSTOR, and the 1945 Scripta Mathematica issue was not obtained. The bibliographic details come from the reference list of the Wikipedia article "Balance puzzle", which was read in full. Dyson's paper is widely said to give the first scheme in which every weighing is fixed before any of them is made. THIS APP DOES NOT ASSERT THAT ON DYSON'S AUTHORITY, because the paper was not read. The fixed-in-advance maxima shown in the app are produced by an exhaustive search that runs in your browser. [MEASURED] WHAT IS COMPUTED, NOT QUOTED ---------------------------- Every number the app displays is searched, in the page, at load time: * the counting bound, from the number of distinguishable outcome vectors; [DERIVED] * the largest number of coins each number of weighings can handle, by exhaustively searching decision trees — the closed form is only ever compared against;[MEASURED] * the same maximum for schemes whose weighings are all fixed in advance, by exhaustively searching sets of weighing codes; [MEASURED] * the enumeration of legal opening weighings behind the parity argument; [MEASURED] * the search costs quoted at the bottom of the "The limit" tab. [MEASURED] Offline, tools-harness.js re-derives all of it and checks it against a second, shared-nothing brute force that works on concrete coins and simulated physical weights, and against an adversary that takes a finished strategy and hunts for two situations it cannot tell apart. WHAT DIFFERS FROM THE ORIGINAL PUZZLE ------------------------------------- 1. The original is a puzzle on paper with fixed parameters. This is an interactive scale where the number of coins, the number of weighings and the variant are all yours to set. 2. Five variants are playable side by side, not one: fake of unknown direction; the same with a coin known to be genuine; identify the coin without naming its direction; fake known to be heavy; and "one fake or none at all". They are genuinely different problems with different answers, and the app says so. 3. A "devious" scale, which is not in the original. No coin is counterfeit until it has to be: the scale answers whichever way keeps the most stories alive. A guaranteed strategy still wins in par; a lazy weighing is punished at once. 4. A live readout of how many stories are still alive against how many futures your remaining weighings can tell apart — the information-theoretic content of the puzzle, shown rather than left implicit. 5. A hint button that plays an optimal weighing taken from the same exhaustive search. 6. A whole tab of searched results that the puzzle itself does not contain. 7. The artwork, the balance, the coins and the layout are original drawings made for this bundle with PIL and the 2D canvas; nothing is traced or imported. TRADEMARK --------- No clearance is claimed, because no register could be queried on 2026-09-19: the USPTO trademark search API returned HTTP 404; EUIPO eSearch plus returned only its JavaScript shell with no records; the WIPO Global Brand Database sat behind a CAPTCHA; and this session's web-search budget was exhausted before a plain search could be run. "Coin Weighing" is used here as a plain descriptive name for a public-domain mathematical puzzle, not as a mark, and no affiliation with anyone is implied or claimed. If you hold a mark you believe is affected, the app is unlisted and can be renamed or withdrawn on request. LICENCE ------- The code and artwork in this bundle are MIT licensed — see LICENSE.txt. The puzzle is public domain. The app runs entirely in your browser: no account, no network calls, no model, no telemetry, nothing leaves the page.