A set of 101 coins consists of 100 genuine coins of equal weight plus one fake coin which is either
a. lighter
OR
b. heavier
than a genuine one.
Using only equal-arm-balance, please determine in two weighings whether it is a. or b.
IMHO it is a nice puzzle, but I doubt whether the result has any practical meaning.
Objections? Let my know.
Source: Leningrad Math. Competition, former USSR.
Divide the coins into 4 groups A33, B33, C33, D2, of labeled count.
Step 1: Weight A33 against B33.
If the result is level:
Step 2: you know you have have 66 good coins in A33 together with B33.
Chose 35 of them and weigh them against corrupted (C33 and D2) and you will
learn "a" or "b" from the behavior of side C,D, lighter or heavier.
Alternatively, in Step 1:
If one side goes up, call this side Up33, and the other Down33.
Step 2 (alternate): you have 33 good coins in C33 and 2 good coins in D2
weigh Up33 against C33. If it is level, then it is "b", a heavier coin in Down33,
If Up33 still goes up, it is a, a lighter coin in Up33. (Up33 can not go down).
Edited on April 18, 2022, 7:40 am
soln
