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Solution to: Coin Weighing

There are several ways to solve this problem. An elegant solution is shown below. Note again that in advance, you do not know whether the coin with different weight is heavier or lighter!

Number the coins from 1 up to 12. Perform the following three weighings:

Left side:Right side:
Weighing 1:1  2  3  104  5  6  11
Weighing 2:1  2  3  117  8  9  10
Weighing 3:1  4  7  103  6  9  12

Call the outcome of a weighing "L" if the left side is most heavy, call the outcome "R" if the right side is most heavy, and call the outcome "B" if the left and right sides have the same weight. Then the following outcomes are possible:

Weighing 1:Weighing 2:Weighing 3:Different coin:
LLL1 heavier
LLR3 heavier
LLB2 heavier
LRL10 heavier
LRB11 lighter
LBL6 lighter
LBR4 lighter
LBB5 lighter
RLR10 lighter
RLB11 heavier
RRL3 lighter
RRR1 lighter
RRB2 lighter
RBL4 heavier
RBR6 heavier
RBB5 heavier
BLL9 lighter
BLR7 lighter
BLB8 lighter
BRL7 heavier
BRR9 heavier
BRB8 heavier
BBL12 lighter
BBR12 heavier

Note: outcomes LRR, RLL, and BBB are not possible.



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