176. "Square" Dad. Having once entered into a legal marriage in California, my neighbor has now reached an age that is a perfect square. The product of the digits representing the father's age equals the age of his wife. The age of their daughter is equal to the sum of the digits in the father's age, and the age of their son is equal to the sum of the digits in the mother's age. How old is each member of the family?
176. The fact that the marriage was legal reduces the number of possible options to three*

| 64 | 10 |  | 49 | 13 | 36 | 9 |
| ---: | ---: | ---: | ---: | ---: | ---: | ---: |
| 24 | 6 |  | 36 | 9 | 18 | 9 |

If we now compare the ages of the children with the ages of the parents, we will find a single possible option, namely: the father is currently 49, the mother is 36, the daughter is 13, and the son is 9 years old. Although it is interesting to note that $1+3=4$, and there are also four members in the family, 13 is not a perfect square and thus violates the family's universal "squareness." These numbers have another interesting property: the sum of the mother's and daughter's ages equals the father's age.