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Re: Triangle riddle
Posted:
Apr 6, 2002 12:17 AM


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



