Difference between revisions of "2012 UNCO Math Contest II Problems/Problem 6"
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== Solution == | == Solution == | ||
| − | <math>180 | + | <math>180</math> |
600 = 2^3 * 3 * 5^2 | 600 = 2^3 * 3 * 5^2 | ||
| − | + | let make possible pairs so : | |
| − | 2 of the digits has to be 5,5 | + | 2 of the digits has to be 5,5 . |
| + | |||
| + | |||
| + | |||
3 digits are left with 2^3 *3 so pairs are : | 3 digits are left with 2^3 *3 so pairs are : | ||
| − | (8,1,3),(4,2,3),(6,4,1) | + | (8,1,3),(4,2,3),(6,4,1) |
| − | ANSWER IS | + | ANSWER IS 5! /2! *3 = 180 |
== See Also == | == See Also == | ||
Latest revision as of 13:30, 26 August 2025
Problem
How many 
-digit positive integers have the property that the product of their digits is 
?
Solution
600 = 2^3 * 3 * 5^2
let make possible pairs so : 2 of the digits has to be 5,5 .
3 digits are left with 2^3 *3 so pairs are :
(8,1,3),(4,2,3),(6,4,1)
ANSWER IS 5! /2! *3 = 180
See Also
| 2012 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 5 |
Followed by Problem 7 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
| All UNCO Math Contest Problems and Solutions | ||
