If you have a chain of links of equal lengths whose ends are connected (so that it forms a loop) then by holding three points and "pulling" them outwards different triangles can be formed. For example, with a chain that has three links 1 triangle can be made. With 4 links no triangles can be made. With 9 links three can be made {(3,3,3),(2,3,4),(1,4,4)} ... I made a program to search through all numbers of links up to 1000000 and look for chains that give the same amount of triangles as there are links. The result was that there's only one - a chain of 48 links can make 48 triangles. And interestingly, numbers lower than 48 give less triangles than links and numbers over 48 give more. By numbers like 1000 you get about 10^6 triangles... also if you take some number of links and keep on multiplying it by the same number, then the number of triangles changes in a fixed pattern. And for every chain, if you either add or subtract 3 links you get the same number of triangles...(adsbygoogle = window.adsbygoogle || []).push({});

Is there any significance to all this or is it just silly number games?

Thanks.

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# I got an interesting resut

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