# When the numbers $8, 11, 18, 20, 23, 32, 38$ are placed to form an equality in the empty boxes below, which one of the numbers will not be used?

When the numbers $$8, 11, 18, 20, 23, 32, 38$$ are placed to form an equality in the empty boxes below, which one of the numbers will not be used?

I tried to distribute the 4 biggest number ($$38+20 + \_ = 32+23 + \_$$ ) into the boxes first. Then I placed $$8$$ and $$11$$, respectively, into the empty boxes left. Finally, I was left with the number that doesn't fit: $$18$$.

Luckily this worked for me, but I don't know what would I do if the "unused" number were one of the biggest numbers.

What is the technique to tackle this problem considering this is a problem given to high school students?

There's a trick to this particular problem: every number in the list is $$1$$ less than a multiple of $$3$$ except for $$18$$. If you use $$18$$ somewhere, the side with $$18$$ will be $$2$$ less than a multiple of $$3$$ and the other side will be a multiple of $$3$$, so that can't work.