5.D.3 FALSE COINS WITH A WEIGHING SCALE
H. S. Shapiro, proposer; N. J. Fine, solver. Problem E1399 -- Counterfeit coins. AMM 67 (1960) 82 & 697 698. Genuines weigh 10, counterfeits weigh 9. Given 5 coins and a scale, how many weighings are needed to find the counterfeits? Answer is 4. Fine conjectures that the ratio of weighings to coins decreases to 0.
Kobon Fujimura & J. A. H. Hunter, proposers; editorial solution. There's always a way. RMM 6 (Dec 1961) 47 & 7 (Feb 1962) 53. (c= Fujimura's The Tokyo Puzzles (Muller, London, 1979), prob. 29: Pachinko balls, pp. 35 & 131.) Six coins, one false. Determine which is false and whether it is heavy or light in three weighings on a scale. In fact one also finds the actual weights.
K. Fujimura, proposer; editorial solution. The 15 coin puzzle. RMM 9 (Jun 1962) & 10 (Aug 1962) 40 41. Same problem with fifteen coins and four weighings.
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