2005 PMWC Problems/Problem I6
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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 | ||
