Solution for #13

If the product of his three children's ages is 72, there are the following possibilities:

         1 *  1 * 72 = 72
         1 *  2 * 36 = 72
         1 *  3 * 24 = 72
         1 *  4 * 18 = 72
         1 *  6 * 12 = 72
         1 *  8 *  9 = 72
         2 *  2 * 18 = 72
         2 *  3 * 12 = 72
         2 *  4 *  9 = 72
         2 *  6 *  6 = 72
         3 *  3 *  8 = 72
         3 *  4 *  6 = 72 

Isaac later gives Albert the sum of their ages, but we don't know what number he says. We do, however, know that Albert can't figure it out from that information. So, we take the possibilities listed above and add them up:

         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 

The only way Albert wouldn't be able to figure out Isaac children's ages by knowing the sum is if the sum was 14, because there are two possibilities. So either the children's ages are 2, 6, and 6, or 3, 3, and 8. But Isaac points out that he has a youngest child. So the ages must be 2, 6, and 6.