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More scales

 
Stan James
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This was on Car Talk last Saturday ...

You have 7 stacks of 100 coins each - total 700 coins. Each stack is either all genuine at 10 grams per coin (1000 per stack) or all fake at 9 grams per coin (900 per stack).

You have a scale that can measure to 0.1 grams accuracy. You don't compare two sets of coins; you just weigh one set and get a number.

How do you find which stacks (zero, some or all) are fake in the fewest weighings? And the hint Ray gave, why is the answer "one"?
 
Nick George
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measure take out 2^n coins from each pile, where n is the pile (i.e. 1 from first pile, 2 from second, 4 from third, etc.) If I'm not mistaken, that should lead to unique numbers. (A bit of handwaving to ward off proof-seekers)
[ May 21, 2004: Message edited by: Joseph George ]
 
Nick George
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so what's the ruling, Stan?
 
Stan James
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Oh, sorry, I thought that one was too easy since first answer was good. Can't fool computer geeks with powers of 2

We had an office in NYC with push button combo locks on the bathroom doors. The men's room combo was 1-2-4-8 and I always thought some geek set that up. Easy to remember tho.
 
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