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King Midas was a very wealthy and powerful king who ruled over 10 states. Each
year each of the states would have to send him, as taxes, a bag fi lled with 100 gold coins. Each
gold coin would have to weigh exactly 4 ounces.
One year after the King received all the bags of gold, with each clearly labeled with the
name of the state it came from, a messenger came running in to the King. He shouted, “Your
Majesty, one of the Governors tricked you. His bag of gold is fi lled with coins that are only
3 ounces per coin instead of 4.” But, before he could utter the name of the Governor or the
state that produced the counterfeit coins, an arrow fl ew through the window and struck him in
the throat. He fell over, dead. So, the King had 10 bags of gold in front of him and no way to
know which contains the counterfeit coins.
Now the King had a scale which is similar to a regular bathroom scale in that it tells you the
total weight placed on it (i.e. 5 ounces, 3 lbs, etc.). And, because he was a very cheap kind of
guy you needed to put a penny into the scale to get a single weighing. Th e King only had one
penny in the whole kingdom so he knew he had to solve this in one weighing.
Question: How was the King going to fi gure out who is the cheating Governor with just one
weighing of the scale?

  • math -

    Put all ten bags on the scale and then remove them one by one. Watch for a drop of 300 oz instead of 400. That would be the bag of 3 oz coins. The "penny" scale will count that as one weighing.

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