A particular triangle

I have a puzzle that I'm unable to find any information on Internet (I have also some difficult to find keywords to search... I have to dispose first n natural numbers in a triangular shape, with the following characteristic: any number must be the subract of the above two. For example, if I want to dispose first 3 number, an obvious solution is:

3 2 1

(1=3-2). If I have to dispose first 6 numbers, a possibile solution is:

1 6 4 5 2 3

(5=6-1, 2=4-2 and 3=5-2). Several solutions are possibile (how many?).

With 15 numbers, solution is not trivial (try it . But the real problem is: is it possibile to generalize construction of these triangles with *any* (triangular) number? Also, any link to this problem will be appreciated.

Thanks in advance.

Look into: http://members.aol.com/bitzenbeitz/Contests/Triangles/ Description.html and to other links from there.

You get repeated numbers, of course, and they're not even close to the range 1..n.

Tue, 12 Nov 2002 01:04:48 +0200, Yirmy ha scritto ben 92 righe per dire:

Metabolizing it...