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Topic: Ingram's Family (Read 1023 times) |
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K Sengupta
Senior Riddler
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Ingram's Family
« on: Feb 3rd, 2006, 9:53pm » |
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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?
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| « Last Edit: Feb 10th, 2006, 11:31pm by K Sengupta » |
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JocK
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Re: Ingram's Family
« Reply #1 on: Feb 4th, 2006, 1:24am » |
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A straightforward solution based on (8*2)^2 = 2^8 is: seven children aged 4, 2, 2, 2, 2, 2, and 2.
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solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it.
xy - y = x5 - y4 - y3 = 20; x>0, y>0.
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fatball
Senior Riddler
Can anyone help me think outside the box please?
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Re: Ingram's Family
« Reply #2 on: Feb 4th, 2006, 11:24am » |
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I have found 5 more solutions:
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.
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pex
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Re: Ingram's Family
« Reply #3 on: Feb 4th, 2006, 12:22pm » |
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For what it's worth:
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
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JohanC
Senior Riddler
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Re: Ingram's Family
« Reply #4 on: Feb 4th, 2006, 2:11pm » |
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on Feb 4th, 2006, 12:22pm, pex wrote:
Up till now, you encountered the only answer with all ages different. Maybe that was the original puzzle's intention?
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JocK
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Re: Ingram's Family
« Reply #5 on: Feb 4th, 2006, 5:11pm » |
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on Feb 4th, 2006, 2:11pm, JohanC wrote:
Up till now, you encountered the only answer with all ages different. Maybe that was the original puzzle's intention? |
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Yep, the riddle requires some additional constraint, something like: "the Ingram's have no twins and all children are their own natural children"...
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IP Logged |
solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it.
xy - y = x5 - y4 - y3 = 20; x>0, y>0.
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K Sengupta
Senior Riddler
Gender:
Posts: 371
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Re: Ingram's Family
« Reply #6 on: Feb 10th, 2006, 11:32pm » |
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Necessary amendments incorporated in the problem body.
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