Could you please help me with the following puzzle:
Consider the following puzzle:
Suppose there are two box makers: Knight and Knave. Knight always writes true statements on his box, while Knave always writes false ones.
(ed: Each box was made by either a knight or a knave, and each one has a note written by its maker -- comments from MJD)
Suppose there are three boxes: A, B, and C. One of the box contains a bomb. The boxes have the following note:
A: There is a bomb in this box.
B: The bomb is not in this box.
C: At most one of these three boxes was made by Knight.
Suppose your task is to avoid choosing a box that contains bomb. Which one should you choose?
My conclusion is that we should choose box C. I derive the conclusion from:
1) Assume that the note in box C is correct.
It means there can only be one box that has correct note i.e. the box C itself. The two other boxes have incorrect notes which mean the bomb will be on box B.
2) Assume that the note in box C is wrong.
This means there will be two (or three boxes) that have correct note. But not all three boxes are correct, because we already assume box C has incorrect note. So, only box A and box B that have the correct note. In this case, it means the bomb is in box A.
So, for both case, the safe choice would be box C. Is this a correct logic reasoning in math?
PS: Additionally, is this a correct way to answer this question? Or is there a more formal way (mathematically)?
Thanks a lot for the help.