Problem 4. A student has 144 balls, which they distribute into four boxes, following these rules:

a) the number of balls in the first box differs by 4 from the number of balls in the second box;

b) the number of balls in the second box differs by 3 from the number of balls in the third box;

c) the number of balls in the third box differs by 2 from the number of balls in the fourth box;

d) the first box contains the most balls.

What is the maximum number of balls the student can put in the second box?

Working time 2 hours.

Each problem is worth 7 points.

## National Mathematics Olympiad  Local Stage, Iaşi
Problem 4. We have the following cases for distributing the balls into the four boxes:

a) $a, a-4, a-1, a-3 \Rightarrow 4 a-8=144 \Rightarrow a-4=34$....................................................................... 2 p

![](https://cdn.mathpix.com/cropped/2024_06_07_78d9298f1c462f888351g-2.jpg?height=60&width=1551&top_left_y=2190&top_left_x=298)

c) $a, a-4, a-7, a-9 \Rightarrow 4 a-20=144 \Rightarrow a-4=37$.................................................................. $2 p$

The second box can contain a maximum of 37 balls............................................................. 1 p