1st hint :
If we multiply the 3 ages, we have 36.
There are 8 solutions, 4 with twins (in red) :
1 x 1 x 36
1 x 2 x 18
1 x 3 x 12
1 x 4 x 9
1 x 6 x 6
2 x 2 x 9
2 x 3 x 6
3 x 3 x 4
2nd hint :
If you sum their ages, we have the Mathematician’s girl age.
1 + 1 + 36 = 38
1 + 2 + 18 = 21
1 + 3 + 12 = 16
1 + 4 + 9 = 14
1 + 6 + 6 = 13
2 + 2 + 9 = 13
2 + 3 + 6 = 11
3 + 3 + 4 = 10
So, of course, if he doesn’t know at that point, that means his daughter is 13 and so, there are still 2 possibilities.
3rd hint :
Saying that his oldest daughter has blue eyes, the Philosopher gives the answer.
Between the 2 solutions, the 2nd one has an older daughter who is 9.
The answer is : The three girls are 2, 2 and 9.
