Question 18
(ROM 4) For any integer $r\ge1$, determine the smallest integer $h(r)\ge1$ such that for any partition of the set $\{1,2,\ldots,h(r)\}$ into $r$ classes, there are integers $a\ge0$, $1\le x\le y$, such that $a+x,a+y,a+x+y$ belong to the same class.