Question

There are three boxes in front of you. They are as follows: – BOX A, which has the following statement written on it: “Box C is empty.” – BOX B, which has the following statement written on it: “This box contains $100.” – BOX C, which has the following statement written on it: “Box B is empty.” One of the three contains $100 and the other two are empty. The box with the money has a true statement on it, while the empty boxes have false statements on them. Which box has the money?

Answer 1

Box C has money.

1.) Box A

It has the statement written : "Box C is empty" , which is false and hence Box A is empty.

2.) Box B

It has the statement written : "This box contains $100" , which is again false and hence this box is empty as well.

3.) Box C

It has the statement written : "Box B is empty" , which is indeed true and hence it contains the money.

In this question , the question arises as to how do we actually decide :

Easy !

Just assume first , as I did that the money is in Box A. According to the hypothesis then, Box B and Box C must be empty and also has statements written on them must be false. I notice the statement on Box C, which says Box B is empty, which indeed is , giving us a contradiction.

Similarly if I assume the money to be in Box B , statement on Box A turns out to be true , whereas it has to be false.

After checking for A and B , I actually moved on to check C and bingo! I got the answer.