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Spoiler for Spolier added
You need 3 or 4 weighings
Divide into 3 heaps - 17, 17, and 16 and weigh the first two. You now know which heap has the fake coin.
Repeat process with the selected heap - 6,6,5 or 5,5, 6 as the case may be, and weigh the first two.
Repeat again 2,2,2 or 2,2,1. If the single coin is fake, no further weighing is required. Else
You have to do a 4th weighing if the fake coin is in a group of 2.
Divide into 3 heaps - 17, 17, and 16 and weigh the first two. You now know which heap has the fake coin.
Repeat process with the selected heap - 6,6,5 or 5,5, 6 as the case may be, and weigh the first two.
Repeat again 2,2,2 or 2,2,1. If the single coin is fake, no further weighing is required. Else
You have to do a 4th weighing if the fake coin is in a group of 2.
