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.