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        riddles >> hard >> Ingram's Family
        
(Message started by: K Sengupta on Feb 3^rd, 2006, 9:53pm)

Title: Ingram's Family
Post by K Sengupta on Feb 3^rd, 2006, 9:53pm

I am looking for an Algebraic Solution to the under noted problem which I found in a puzzle book.

PROBLEM:

The product of the ages of Ingram’s children is the square of the sum of their ages. Ingram has less than eight children . None of his children are more than 14 years old. All the ages of his children are different. All of his children are at least two years old. All the ages are expressed in integral number of years. How many children are there? What are their ages?

Title: Re: Ingram's Family
Post by JocK on Feb 4^th, 2006, 1:24am

A straightforward solution based on [hide](8*2)^2 = 2^8[/hide] is: [hide]seven children aged 4, 2, 2, 2, 2, 2, and 2[/hide].

Title: Re: Ingram's Family
Post by fatball on Feb 4^th, 2006, 11:24am

I have found 5 more solutions:
[hide]6 children: 4,4,2,2,2,2
5 children: 12,6,2,2,2
4 children: 4,4,4,4
3 children: 9,9,9
No solution for 2 children or less.[/hide]

Title: Re: Ingram's Family
Post by pex on Feb 4^th, 2006, 12:22pm

For what it's worth:
[hide]5 children: 2, 2, 4, 4, 4
4 children: 2, 4, 6, 12
4 children: 2, 5, 5, 8
4 children: 3, 3, 6, 6[/hide]

Title: Re: Ingram's Family
Post by JohanC on Feb 4^th, 2006, 2:11pm

on 02/04/06 at 12:22:03, pex wrote:

[hide]4 children: 2, 4, 6, 12
[/hide]

Up till now, you encountered the only answer with all ages different. Maybe that was the original puzzle's intention?

Title: Re: Ingram's Family
Post by JocK on Feb 4^th, 2006, 5:11pm

on 02/04/06 at 14:11:06, JohanC wrote:

Up till now, you encountered the only answer with all ages different. Maybe that was the original puzzle's intention?

Yep, the riddle requires some additional constraint, something like: "the Ingram's have no twins and all children are their own natural children"...

Title: Re: Ingram's Family
Post by K Sengupta on Feb 10^th, 2006, 11:32pm

Necessary amendments incorporated in the problem body.