# Presentation with sequence KOBON TRIANGLES PROBLEM

Alexandre Wajnberg alexandre.wajnberg at skynet.be
Sun Nov 20 17:40:24 CET 2005

```
----->>>  WITH THE IMAGE!!!

> David Wilson wrote:
>> See problem 3 of
>> http://www.stetson.edu/~efriedma/papers/planar.ppt
>>
>> for a sequence.  I did not find it in the OEIS, maybe the OEIS has a
>> corrected version?

Ed Pegg wrote:
> http://mathworld.wolfram.com/KobonTriangle.html
> http://www.research.att.com/projects/OEIS?Anum=A006066
>
> n=15 was recently solved, but n=10 to n=14 are still unsolved.

I propose a solution for n (or K) = 10 : 25 triangle. Cf image attached.
It's one unit below the theoretic maximum (Floor[n(n-2)/3]) thus 26, like
for n=6 and 8.

n=. . . . . . . 3 4 5 6 7  8  9  10 11 12 13 14 15
K(n): . . . . . 1 2 5 7 11 15 21 25 ?  ?  ?  ?  65
Max possible: . 1 2 5 8 11 16 21 26 33 40 47 56 65

Conjecture:
-for n odd,     K(n)=the max. possible
-for n even >4, K(n)=the max.-1

Alexandre

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