Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.
|
|
|
|
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
|
|
|
|
