FILE No.82Unsolved
Confiscated coins are in ten heaps, each with plenty of coins. Exactly one heap is made entirely of fakes.
A genuine coin weighs 10 g and a fake 9 g. They look identical. You have one accurate digital scale and may weigh only once.
How can one weighing tell you which heap is fake?
If you get stuck, open the hints one at a time, in order.
If you take the same number of coins from every heap, does the shortfall tell you which heap?
What if you take a different number from each heap?
Match the shortfall in grams to the heap number.
How can one weighing tell you which heap is fake?
Choose the answer closest to the truth.
Take 1 coin from heap 1, 2 from heap 2, ... 10 from heap 10, weigh them all together, and read the heap from how many grams light
The answer is: take 1 coin from heap 1, 2 from heap 2, ... 10 from heap 10, weigh them all together, and read the heap from how many grams light.
You take 1 + 2 + ... + 10 = 55 coins. If all were genuine they would weigh 550 g. If heap k is fake, k fake coins are in the pile, so the total is k grams light. A weight of 547 g means heap 3 is fake.
Taking the same number from each heap makes it impossible to tell the heaps apart.
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