2008 UNCO Math Contest II Problems/Problem 5

Problem

5. The sum of $400, 3, 500, 800$ and $305$ is $2008$ and the product of these five numbers is $146400000000 = 1464 \times 10^8.$

(a) Determine the largest number which is the product of positive integers whose sum is $2008$ .

(b) Determine the largest number which is the product of positive integers whose sum is $n$ .

(a) $3^{668}\cdot 2^2$ (b) $3^k$ if $n=3k$ ; $2^2\cdot 3^{k-1}$ if $n=3k+1$ ; $2\cdot 3^{k}$ if $n=3k+2$

2008 UNCO Math Contest II (Problems • Answer Key • Resources)
Preceded by Problem 4	Followed by Problem 6
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10
All UNCO Math Contest Problems and Solutions