The Three Boxes
There are three boxes: a lead box, a silver box, and a gold box. One box has gold in it. Their labels read as follows:
-The lead box: The gold is not in this box.
-The gold box: The gold is in this box.
-The silver box: The gold is in the gold box.
If exactly one label is true, which box is the gold in?
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1 solution
The lead box: The gold is not in this box. => This statement is true.
The gold box: The gold is in this box. => This statement is false.
The silver box: The gold is in the gold box. => This statement is false.
Let us assume:
If the first statement is true , then the second and third statements may be false. (which follows:Only one label/statement is true)
If the second statement is true , then it agrees with the first and third statements making all true, which cannot be since only one label/statement is true.
If the third statement is true , then it agrees with the first and second statements making all true, which cannot be since only one label/statement is true.
Thus, only the first statement is true.
If the gold is not in the lead box (which is true), then it must be in either gold or silver box. Since if the gold is in the gold box... (look at 2nd assumption above) But if the gold is in the silver box, everything makes sense.
Therefore, the gold is in the silver box.