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Divide the coins into two sets of eight coins and one set of one coin. Compare the two sets of 8. If one set is heavier, see Case 1. If the sets are equal, see Case 2.
Case 1: One set of eight is heavier.
That set must have at least three heavier coins. Divide that set into two sets of four and compare the sets of four. Label the coins from the heavier set of four A, B, C, D. If the sets are equal, take either set. Weigh A/B and B/C. See the table below for results:
A/B|B/C| Must be heavy
---+---+-------------
= > A and B
= < C and D
> = A and D
> < A and C
< = B and C
< > B and D
= = A, B and C
Case 2: Both sets of eight are equal.
The 17th coin is heavy and there are two heavy coins in each set of eight. Only one heavy coin from a set of eight is needed. Take one of the sets of eight and divide it into two sets of four and compare the sets of four. If one set of four is heavier see Subcase 2.1. If the sets of four are equal, see Subcase 2.2.
Subcase 2.1: One set of four is heavier.
That set of four must contain two heavy coins. Label the coins in that set A, B, C, D and weigh A/B and B/C. Use the table in Case 1 (ignore the =/= option) to get two heavy coins.
Subcase 2.2: The sets of four are equal.
Each set of four has one heavy coin. Choose one set and label its coins A, B, C, D. Weigh A/B and C/D. One weighing will be heavy, take that heavy coin and the 17th coin for two heavy coins. |
