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Merger proposal
editI see the article Eight ball problem which is very similar (only different variant) with the more general article, Balance puzzle. I propose that "Eight ball problem" to be merged with "Balance puzzle". -- Chaotic iak (talk) 12:04, 22 January 2011 (UTC)
Self-contradiction?
editThe article states (with citation) that n weighings are sufficient to find a bad coin among (3^n − 1)/2 coins, but then goes on to show that two weighings are sufficient for nine coins, three for 27 coins, and four for 81 coins (in other words, n weighings are sufficient for 3^n coins). Perhaps the first formula is for a more general problem than the one being discussed, but that isn't clear at all from the text. Does anyone know the story here? MrRK (talk) 19:56, 3 August 2017 (UTC)
Information gain strategy
editAs described in the late David MacKay lecture about information theory, one strategy to solving the puzzle is looking at entropy (average information gain) and trying to maximize it as much as possible. This is perhaps the explanation for the generalized "base-three numbering" technique, and the actual solution given (for the 12 coins problem) follows it as well, as every weighing maximizes the entropy. I have heard this puzzle a few times, and it was always in regards to entropy - yet this term never comes up in the article, which I think is a big miss.
14 coins in 3 weights
editI found a solution to 14 coins in 3 weights, where the target coin is different from others. The trick is to divide two coins in half so you can compare 4 and 5 coins. Check it out here: https://math.stackexchange.com/a/3948327/101178
The redirect Definitive solution to the counterfeit coin problem has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at Wikipedia:Redirects for discussion/Log/2023 June 24 § Definitive solution to the counterfeit coin problem until a consensus is reached. Muhandes (talk) 23:01, 24 June 2023 (UTC)
The redirect Definitive Solution to the Counterfeit Coin Problem has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at Wikipedia:Redirects for discussion/Log/2023 July 2 § Definitive Solution to the Counterfeit Coin Problem until a consensus is reached. Jay 💬 08:09, 2 July 2023 (UTC)
first table
editI suggest to rewrite the second goal as "identify the coin and its nature" 151.29.39.54 (talk) 06:15, 23 November 2024 (UTC) more correctly "identify the coin and weather is lighter or heavier" — Preceding unsigned comment added by 151.29.39.54 (talk) 11:02, 23 November 2024 (UTC)
I feel that in the second case one should have known = "at most one is different" and the goal should de modified accordingly. — Preceding unsigned comment added by 151.29.39.54 (talk) 09:55, 25 November 2024 (UTC)
12 coins
editIn the easily-scalable method I label
000 - 001 - 002 - 010 - 011 - 012 - 020 - 021 - 022 - 100 - 101 - 102
at the second step I find on the left pan (0) 000-001-002-100-101-102 and on the right one (2) 020-021-022, that is clearly useless. Perhaps the pans 1 and 0 are inverted @Daveagp: 151.29.39.54 (talk) 12:19, 23 November 2024 (UTC) Even worse, at the third step I have 9 coins on pan 0. Should I start by 001? No, I would have 8, still a useless measure. Perhaps 1/0 are inverted and must start from 001.
I have tried 001 ... 110, but at step 2 I have 5-4-3 coins on the pans. — Preceding unsigned comment added by 151.29.39.54 (talk) 15:15, 23 November 2024 (UTC)