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#1068134 - Wed Oct 08 2014 11:17 AM Birds in a tree
baldhair Offline
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Registered: Tue Aug 05 2014
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Loc: Gloucestershire UK
Fred has three daughters. When I asked him their ages he said - never one to give a straight answer, our Fred - "If you multiply their three ages together the answer is 90, and they are all under 15. The sum of their ages equals the number of birds in that tree." So I counted the birds in the tree, but I still didn't know their ages. How many birds were there in the tree?

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#1068146 - Wed Oct 08 2014 11:56 AM Re: Birds in a tree
flopsymopsy Online   content

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Sixteen?
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#1068171 - Wed Oct 08 2014 02:44 PM Re: Birds in a tree
Lottie1001 Offline
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or fourteen?

3x5x6=90
3+5+6=14
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#1068175 - Wed Oct 08 2014 02:50 PM Re: Birds in a tree
mehaul Offline
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Registered: Wed Feb 03 2010
Posts: 6516
Loc: Florida USA
1+9+10=20 answer
1x9x10=90
========
2+5+9=16 answer
2x5x9=90
========
3+3+10=16 answer
3x3x10=90
========
3+5+6=14 answer
3x5x6=90
========
If the Answers were 20 or 14, you would know what the ages were (1,9,10 or 3,5,6). Since you don't know the answer with those possible combinations, the ages of the girls must be something other than either of those possibilities. But, since knowing the number of birds in the tree doesn't completely define the answer and leaves you 'up the tree' as it were, either (2,5,9) or (3,3,10) are the ages. In either of those cases, their ages total 16 and the multiplication result is 90. So, their ages are either 2, 5 and 9 or 3, 3 and 10, and the number of birds in the tree is 16 as flopsy says.

In other words, knowing the count of birds in the tree to be 16, you still cannot be sure of the breakdown of their ages since there are two possibilities that add up to 16.
If the number of birds was 20, you would know the age distribution.
If the number of birds was 14, you would know the age distribution.
It is the not knowing the distribution that imposes a correct bird count to be 16.


Edited by mehaul (Wed Oct 08 2014 02:56 PM)
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#1068291 - Thu Oct 09 2014 12:25 PM Re: Birds in a tree
baldhair Offline
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Registered: Tue Aug 05 2014
Posts: 81
Loc: Gloucestershire UK
Sixteen it is. That was a very comprehensive answer, mehaul. And correct of course.
Factorise 90, factors less than 15.
Possibles are:
1 x 9 x 10 (sum 20)
2 x 5 x 9 (sum 16)
3 x 5 x 6 (sum 14)
3 x 3 x 10 (sum 16)
After having done this, I still don't know their ages; so there must be two possibilities,i.e. 2 x 5 x 9 and 3 x 3 x 10, both adding to 16.
So there must be 16 birds in the tree.
If the answer was 14, Lottie, we'd know that the children's ages were 3, 5 and 6. But we don't.
Thanks for the input.


Edited by baldhair (Thu Oct 09 2014 12:29 PM)
Edit Reason: explanation

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#1068324 - Thu Oct 09 2014 07:52 PM Re: Birds in a tree
Anton Offline
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Registered: Sat May 03 2008
Posts: 926
Loc: California USA
Nevermind. Forgot to include a variable.


Edited by Anton (Thu Oct 09 2014 07:53 PM)

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