Counting The Spots
Standard six-sided dice are numbered from 1 to 6 and are designed to have opposite sides add up to 7. (For example, a 3 on the top means a 4 is hidden on the bottom.) When you roll a die, there are 5 visible faces and 1 invisible face.
You roll two dice and count the number of spots on ALL visible faces, getting a total of 40. What is the sum of just the top faces?
The answer is 12.
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Adding up every face on both dice gets 2 ( 1 + 2 + 3 + 4 + 5 + 6 ) = 2 ( 2 1 ) = 4 2 .
Since the visible sum is 40, the hidden faces must be showing a sum of 2. That is, the dice show 1 and 1 on the bottoms. Since they add up to 7 with their opposite sides, that means the tops of the dice must be 6 and 6.