I happen to be the King of Jericho and each year I receive 10 gold bars from
each of 10 Barons in my Kingdom. My spies inform me that this year, one of
the Barons will try to save money by shaving 1 gram from each of his bars.
A legitimate bar weighs 100 grams, but there's no way to tell the difference
between a legitimate bar and a shaved bar except by weighing.
The Puzzle: I have a crusty old coin-operated "speak your weight" machine, and, being a bit cheap, I only want to use it once. How can I tell which Baron has been cheating me with only one weighing?
Hints and solutions below:
Hints will appear here!
There's no trick involved, just a weighing! As you can only make one weighing, you'll have to weigh some gold bars from each of the 10 piles.
You don't have to take the same number of bars from each pile.
Take 1 bar from the first pile, 2 from the second, and so on. If my spy was wrong, I'd end up with 100+200+...+1000=5500 grams of gold. But if the first Baron shaved his gold, I'll have 10 grams less, or 5490 grams. If the second Baron cheated, I'll have 5480 grams, and so on.
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