2005 PMWC Problems/Problem I6
Problem
A group of people consists of men, women and children (at least one of each). Exactly apples are distributed in such a way that each man gets apples, each woman gets apples and each child gets apple. In how many possible ways can this be done?
Solution
Subtracting the second equation from the first, we get . Looking at this equation , we see that must be a multiple of 5, so . Thus the choices for are , which gives us possible choices.
See also
2005 PMWC (Problems) | ||
Preceded by Problem I5 |
Followed by Problem I7 | |
I: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 T: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 |