Monday, February 23, 2015
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Solution: The sum of any two opposite faces of a die is 7. So, excluding the top face, the sum of the numbers on the 3-dice tower is always equal to 7 x 2 x 3 = 42, and it doesn't matter how we arrange the dice. The only thing that affects the total sum is the number showing on the top, which can be any number from 1 to 6. So the minimum sum is 42 + 1 = 43 and the maximum sum is 42 + 6 = 48. For 20 dice, the minimum sum is 7 x 2 x 20 + 1 = 281 and the the maximum sum is 7 x 2 x 20 + 6 = 286. For n dice, the minimum sum is 7 x 2 x n + 1 and the maximum sum is 7 x 2 x n + 6.
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