weighings are sufficient
to find a bad coin among coins (Steinhaus 1999, p. 61).
vos Savant (1993) gives an algorithm for finding a bad ball among 12 balls in three
weighings (which, in addition, determines if the bad ball is heavier or lighter than
the other 11), and Steinhaus (1999, pp. 58-61) gives an algorithm for 13 balls.
Bachet's weights problem asks for the minimum number of weights (which can be placed in either pan of a two-arm balance) required to weigh any integral
number of pounds from 1 to 40 (Steinhaus 1999, p. 52). The solution is 1, 3,
9, and 27: 1, ,
3, , , , ,
, 9, , ,
, , , , , , and so on.
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