SOLUTION: Five cubic dice were rolled, and the product of the numbers obtained was 432. What is largest possible sum of five such numbers?

Algebra ->  Probability-and-statistics -> SOLUTION: Five cubic dice were rolled, and the product of the numbers obtained was 432. What is largest possible sum of five such numbers?      Log On


   



Question 911770: Five cubic dice were rolled, and the product of the numbers obtained was 432.
What is largest possible sum of five such numbers?

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
We break 432 into primes:

432 = 2*2*2*2*2*3*3*3

To make the sum as large as possible, we have to get as many of 
the 5 rolls to be 6's as possible.

The most number of 6's we can make by grouping the factors of 432 is 3,
like this

(2*3)(2*3)(2*3)*2

And to make 5 factors we have to use a 1 factor:

432 = 6*6*6*2*1 and 6+6+6+2+1 = 21 is the largest possible sum.

Edwin