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
Got a credit card? use our Credit Card & Finance Calculators
Thanks to Wasron,jfgw,Rhyd6,eyeball08,Wondergirly, for Donating to support the site
Bountiful
-
- The full Lemon
- Posts: 10815
- Joined: November 4th, 2016, 8:17 pm
- Has thanked: 1472 times
- Been thanked: 3006 times
Re: Bountiful
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?
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?
-
- Lemon Slice
- Posts: 553
- Joined: November 9th, 2016, 11:33 am
- Has thanked: 234 times
- Been thanked: 161 times
Re: Bountiful
UncleEbenezer wrote: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
Return to “Games, Puzzles and Riddles”
Who is online
Users browsing this forum: No registered users and 17 guests