Adámek was recalculating his collection of rainbow marbles. He found that he could divide them into equal piles in several ways. If he divided them into three piles, there would be $\mathrm{v}$ more marbles in each pile than if he divided them into four piles.

How many rainbow marbles did Adámek have?

(E. Semerádová)

Hint. Imagine actually regrouping the marbles from four piles into three.
Rearranging the balls from four piles into three can be done by distributing all the balls from one pile into the remaining three.

In each of the three new piles, there were eight more balls than originally, so the pile from which the balls were distributed had 24 balls $(3 \cdot 8=24)$.

All the piles were of equal size and there were originally four, so Adam had 96 balls $(24 \cdot 4=96)$.

Note. If we denote the unknown number of balls in each of the four piles by $k$, then the condition from the problem can be expressed as $4 k=3 \cdot(k+8)$. Expanding this, we get $4 k=3 k+24$, thus $k=24$.