Difference between revisions of "2008 UNCO Math Contest II Problems/Problem 5"
(Created page with "== Problem == 5. The sum of <math>400, 3, 500, 800</math> and <math>305</math> is <math>2008</math> and the product of these five numbers is <math>146400000000 = 1464 \times 10...") |
(→Solution) |
||
| (One intermediate revision by one other user not shown) | |||
| Line 10: | Line 10: | ||
| − | == Solution == | + | == Solution == |
| − | + | (a) <math>3^{668}\cdot 2^2</math> (b) <math>3^k</math> if <math>n=3k</math>; <math>2^2\cdot 3^{k-1}</math> if <math>n=3k+1</math>; <math>2\cdot 3^{k}</math> if <math>n=3k+2</math> | |
== See Also == | == See Also == | ||
Latest revision as of 02:02, 13 January 2019
Problem
5. The sum of 
and 
is 
and the product of these five numbers is
(a) Determine the largest number which is the product of positive integers whose sum is .
(b) Determine the largest number which is the product of positive integers whose sum is 
.
Solution
(a) 
(b) 
if 
; 
if 
; 
if 
See Also
| 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 | ||
