The Return of Combinatorial ... something idk

by agbdmrbirdyface, Nov 28, 2016, 3:05 AM

Another problem, this time from the IMO, that we can kill by Combinatorial Nullstellensatz:
IMO 2007/6 wrote:
Let $n$ be a positive integer. Consider \[S=\{(x,y,z)~:~x,y,z\in \{0,1,\ldots,n \},~x+y+z>0\}\]as a set of $(n+1)^3-1$ points in three-dimensional space. Determine the smallest possible number of planes, the union of which contain $S$ but does not include $(0,0,0)$.

Solution:

Tidbit

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How did the word nullstellensatz originate? :maybe:
This is OP btw, great job :thumbup: even if I can't understand the proof at all :maybe:

by zephyrcrush78, Dec 3, 2016, 4:42 AM

To share with readers my favorite problem I came across today :) (Shout for contrib.)

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