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Topic: Triangle riddle
Replies: 3   Last Post: Apr 12, 2002 3:56 AM

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Randall Rathbun

Posts: 79
Registered: 12/6/04
Re: Triangle riddle
Posted: Apr 6, 2002 12:17 AM
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JonahHex wrote:

> A friend writes to say he bought a little box of midget matches, each
> one inch in length. He found that he could arrange them all in the
> form of a triangle whose area was just as many square inches as there
> were matches. He then used up six of the matches, and found that with
> the remainder he could again construct another triangle whose area was
> just as many square inches as there were matches. And using another
> six matches he could again do precisely the same.
>
> How many matches were there in the box originally? The number is less
> than 40.


Running an exhaustive c program on my linux system shows:

Sides Perimeter/Area
10,8,6 24
13,12,5 30
17,10,9 36
20,15,7 42
29,25,6 60

up to triangles with the largest side <= 500.

So I guess the answer is 36, but 42 would have made 4 such identical
conditions.

Better question - Are these 5 triangles the only ones that exist?

- Randall





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