All One
How did he change all the labels with drawing only ONE coin? Solve this tricky riddle!?
Jesse has three sacks filled with coins. One sack has all nickels; one has all quarters; and the third has a combination of nickels and quarters. All the sacks are labeled, but they are all labeled incorrectly, and he can't see into the sacks. However, by drawing only one coin out of the sack, he can change all the labels to the correct ones. How?
An explanation would be great.
Jesse draws a coin out of the sack labeled "MIXED". If it is a quarter he knows this is the "quarters" sack. It can't be "mixed" as it is labeled "mixed" already and we know it is labeled incorrectly. Obviously it can't be the "nickel' sack. Therefore it has to be the quarter sack.
This then means that as the sacks are labeled incorrectly, it means that the sack labeled nickels can't be "nickels" and it can't be "quarters" as we have just allocated that one to the one labeled "mixed". The only alternative for it is therefore the "mixed" sack. That means that the remaining sack, the one labeled "quarters" is in fact the "nickels", the only denomination not yet allocated.
Similarly if the original coin drawn was not a quarter but was a nickel, the sack labelled "mixed" = nickels
The sack labelled quarters = mixed
The sack labelled nickels = quarters
Therefore as long as a coin is drawn from the sack labeled "mixed" all the sacks can be correctly identified. It doesn't matter which coin is drawn, a quarter or a nickel.
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