Mod question!Mod question!?

yes.

all positive whole numbers (X) are either 3mod0, 3mod1 or 3mod2. if a number is the sum of 3 numbers (x1 +x2+x3) then it only needs five to choose from;

you either have one of each type available to choose from or three of one type. (think about it). either way you have 3 numbers whose total will be a multiple of 3.

i hope i am writing the mod stuff right. long time no see. but the reasoning is sound. by 3mod2 i mean "with 2 remaining when i divide by 3"