Question 265131: Hello here is a word problem i can not figure out called It's in a Box!:
There are two boxes; one marked A and one Marked B. Each box contains either 1 million dollars or a deadly snake that will kill you instantly. You must open one box. On box A a sign reads 'At least one of these boxes contains 1 million dollars" and on box B there is a sign that reads "A deadly snake that will kill you instantly in box A". You are told either both signs are true or both are false. Which box do you open?
I would guess the 1 million is in box B because the sign is attempting to mislead the person.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Let's assume that the two statements are both false. If "At least one of these boxes contains 1 million dollars" is false, then there are no boxes with 1 million dollars. In other words, they both have snakes in them. If "A deadly snake that will kill you instantly in box A" is false, then there isn't a deadly snake in box A. Since the only choices are 1 million dollars or a snake, this means that box A must have 1 million dollars. But this is a clear contradiction of the negation of the last statement. Because of this contradiction, this means that the two statements are NOT false at the same time. So the only choice left is that the two statements are true at the same time. Note: you'll find that no contradiction occurs when the two statements are true.
Because we've shown that the two statements are both true, we now know that box A has a deadly snake in it (due to the statement on box B). So the box to open is box B since this is the only box with 1 million dollars in it.
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