1998 AHSME Problems/Problem 13
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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) | ||
| Preceded by Problem 12 | Followed by Problem 14 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
