Mrs. Lobotomy tells him that they have 3 daughters and 3 sons, that the product of the 3 daughters' ages is the same as their house number, the sum of the 3 daughters' ages is the same as her own age, the product of the 3 sons' ages is also the same as their house number, and the sum of the 3 sons' ages is the same as her husband's age.

The census taker is an accomplished mathematician, but after some time he determines that it is not possible to figure the ages of the sons or the daughters.

Mr. Lobotomy then tells the census taker that the difference in age between the youngest daughter and youngest son is the same as the age of their cat. The census taker does not see a cat, and they have not mentioned its age, but he knows that it still would be impossible to determine the ages of the 6 children.

The cat is 3 years old, and the sum of the ages of the oldest son and the oldest daughter is not 60. What are the ages of the 8 people in the Lobotomy family?