1998 AHSME Problem 13

Number Theory Level 3

Walter rolls four standard six-sided dice and finds that the product of the numbers of the upper faces is 144. Which of he following could not be the sum of the upper four faces?

15 16 18 17

Daniel Hirschberg by Daniel Hirschberg , 39, USA

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2 solutions

Vamshi Paidimarri
Apr 22, 2014

Possible combinations for product 144

a) 6 4 2 3 Sum:16

b) 6 3 4 4 Sum: 17

c) 2 3 4 6 Sum: 15

So, 18 is violated

1 Helpful 0 Interesting 0 Brilliant 0 Confused

6 3 4*4 = 288 and not 144

Jan Chomiak - 4 years, 1 month ago

6 + 6 + 1 + 1 + 2 + 2 = 18

Mayank Holmes - 7 years ago

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There are only 4 dice.

Joe Mansley - 5 years, 8 months ago
Kamal Sharma
Apr 1, 2014

Possible Combination for product 144

a) 4 3 4 3 Sum: 14

b) 6 4 2 3 Sum:15

c) 6 6 2 2 Sum: 16

d) 6 6 4 1 Sum:17

So 18 is the out of the equation.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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