x+y+z=11.
x={ 1,2,3 }, y={ 1,2,3,4 }, z={ 1,2,3,4,5 }
xꜜ z→ |
1 |
2 |
3 |
4 |
5 |
1 |
2 |
3 |
4 |
5 |
6 |
2 |
3 |
4 |
5 |
6 |
7 |
3 |
4 |
5 |
6 |
7 |
8 |
4 |
5 |
6 |
7 |
8 |
9 |
x≠1, because no cell in the above addition table contains 11-1=10.
x=2: (y,z)=(4,5);
x=3: (y,z)=(3,5), (4,4).
Therefore (x,y,z)=(2,4,5), (3,3,5), (3,4,4), three ways to get 11 from 3 positive integers.