Bountiful

[cinelli]

Elderly great grandmother Maud, who had only daughters, realised that each of them had produced as many sons as they had sisters, and no daughters. In turn, each of her grandsons had produced as many daughters as he had brothers. At Christmas she was delighted to recount this to her friends and, furthermore, that the total numbers of her daughters, grandsons and great granddaughters was the same as her age! How old is Maud?

Cinelli

[UncleEbenezer]

Um, far too easy, or I'm missing summat?

N daughters, each with (N-1) sons, each with in turn (N-2) daughters. So by generation, that's N grannies, N(N-1) dads, and N(N-1)(N-2) girls. Total N(1 + N-1 + (N-1)(N-2)), which we can of course reduce at will.

The fact that she's a great granny tells us N-2 > 0, so N is not less than 3. We can evaluate Maud's age for different values of N:
3 15
4 40
5 85
6 156
7 259
8 400

OK, unless she's of Methuselah's blood we've gone far enough. Which of those ages are realistic will depend on Maud's species, and what particular cultural/folkloric tradition she belongs to.


Supplementary question: who are Maud's friends?

[cinelli]

Um, far too easy, or I'm missing summat?

No, you're not missing anything. It was a nice gentle puzzle for Christmas day.

Happy Christmas to all readers.

Cinelli