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.