Puzzle 102 - Solution

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You will be able to find at least 11 genuine coins. To do this, start anywhere and number the coins clockwise around the circle. Put coin 1 on the left pan of the beam balance and coin 11 on its right pan.

If the pans remain balanced, both coins must be genuine because there are only 10 fake coins, which are all in a row. And because there are only 20 genuine coins, and you’ve already found two, the 19 coins in the clockwise segment from coin 12 to coin 30 cannot all be genuine—the streak of 10 fake ones must be within that range. So all 11 coins from coin 1 to coin 11 are genuine.

If the left pan goes down, coin 1 is genuine and coin 11 is fake. The fake coins can only be in the range from coin 2 to coin 20. Therefore, the 11 coins from coin 21 to coin 1 are genuine.

And finally, if the right pan sinks, coin 11 is genuine, and coin 1 is fake. The fake coins can only be in the range from coin 22 to coin 10. Therefore, the 11 coins from coin 11 to coin 21 are genuine.

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