72=2×2×2×3×3
Children ages and sums:
1+1+72=74
1+2+36=39
1+3+24=28
1+4+18=23
1+6+12=19
1+8+9=18
2+2+18=22
2+3+12=17
2+4+9=15
2+6+6=14
3+3+8=14
3+4+6=13
If we know the sum and that sum is only one, we don't need the information about youngest child so sum is 14. Children ages couldn't be 3, 3 and 8 because there is only one youngest child. That means children ages are: 2, 6, 6.
