A chocolate bar is divided into 24 squares by 3 horizontal and 5 vertical notches. We want to break it into pieces by cutting along these notches. With each cut, we can only split one existing piece into two. What is the minimum number of cuts required?
No matter where along the edge we start cutting the chocolate, after the first cut we get two pieces. The next cut again increases the number of chocolate pieces by one. Therefore, after each cut, one new piece always results.

Since we start from $1 \mathrm{piece}$ and we want to end up with $24 \mathrm{pieces}$, we need 23 cuts. This is the minimum number of cuts, but it is also the maximum number of cuts.

Zempléni András (Budapest, I. István Gymnasium)