In Search of the Bogus Coins
RAY: We have seven stacks of coins, each with 100 coins. Real coins weigh ten grams, and phony coins weigh 11 grams. We’re going to weigh the coins on an analytic scale, which works just like your average bathroom scale – but it’s accurate to within a tenth of a gram.
Here’s the rub. Unlike our many fine previous coin puzzlers, in which you have one stack of coins that’s counterfeit, this time you could have several stacks of coins that are counterfeit.
TOM: If one coin in the stack is counterfeit, they’re all counterfeit?
RAY: Yes. But, it could be that none, some or all of the stacks of coins are bogus. You don’t know.
The question is, what’s the fewest number of weighings you need to make, to determine which of the stacks, if any, has counterfeit coins?
TOM: And how come it’s only one weighing?
RAY: Okay, wise guy. That’s right. That’s part two of the puzzler. How come it’s only one weighing – and how are you going to do it?
This is cartalk’s puzzler for this week (April 23rd through April 30th, 2011). If you answer on their website, you could be chosen to win a prize!
Hint: Power of binary numbers.