1998 AHSME Problems/Problem 13
Problem
Walter rolls four standard six-sided dice and finds that the product of the numbers of the upper faces is . Which of he following could not be the sum of the upper four faces?
Solution
We have .
As the numbers on the dice are less than , the two s must come from different dice. This leaves us with three cases: , , and .
In the first case we have , leading to the solutions and .
In the second case we have , leading to the only solution .
In the third case we have , leading to the only solution .
We found all four possibilities for the numbers on the upper faces of the dice. The sums of these numbers are , , , and . Therefore the answer is .
See also
1998 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
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