# midas touch riddle?

THE MIDAS TOUCH

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?

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First he needs to number the bags from 1-10. Then he takes one coin from bag no.1, two coins from bag no.2, three coins from bag no.3, etc. all the way up to ten coins from bag no.10, and weighs the coins he has removed from the bags. 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55, so he is weighing 55 coins. If they all weighed 4 ounces apiece, the total weight would be 55 x 4 = 220 ounces. But the counterfeit coins are each one ounce too light, so the coins he puts on the scale will weigh less than 220 ounces. The number of ounces less than 220 is the same as the number of counterfeit coins, and since he took a different number of coins from each bag, he knows which bag the counterfeits came from, and which governor cheated him.

didnt you mention ealier that the bags were clearly labled from each state?

You put the first bag of coins on the scale check the weight, before removing it place the second bag on the scale and then remove the first. If they weigh the same continue placing a new bag of coins on the scale before removing the previous bag until you find the one that weighs less.

Or you could just look on the bags since they are clearly labeled from which state they came from