Hint to Puzzle #43: 10 Piles of 10 Coins one of Which is Fake.
43. You have 10 stacks of 10 gold coins. All of the coins in one of these stacks are counterfeit, all the other coins are not. A real coin weighs 10 grammes. A counterfeit coin weighs 11 grammes. You have a modern scale that provides an accurate readout. What is the minimum number of weighings needed to determine which stack is fake?
How about if you had 11 stacks?
How about if you had 11 stacks?
Tricky to give a hint to this. Firstly note this is not an old fashioned balance like the previous scales we've used. it's a modern scale that gives an exact weight in grammes. Unusually the answer. The counterfeit pile can be identified perfectly with one weighing. The clever bit is obviously how you go about doing this.The best thing I can suggest is that you number all of the piles and think about how many from each pile need to go on the scales.
The answer includes an example of a real world situation where this technique is used.
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