3. A chessboard consists of $8 \times 8$ squares. In a corner square stands a knight. The knight makes jumps of either two squares horizontally and one square vertically, or two squares vertically and one square horizontally. In each square of the chessboard, we write down how many jumps the knight needs to reach it.

Which number have we then written down the most?
A) 2
B) 3
C) 4
D) 5
E) 6
A3. C) 4

In each field of the chessboard, we write down how many moves a knight needs to get there. We start with 0 in the corner, then write a 1 in the (empty) squares that can be reached from the 0 in one move, then write a 2 in the (empty) squares that can be reached from a 1 in one move, and so on. Eventually, we count how often each number appears and see that 4 is the most frequent number, appearing 21 times (3 appears 20 times).

| 5 | 4 | 5 | 4 | 5 | 4 | 5 | 6 |
| :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- |
| 4 | 3 | 4 | 3 | 4 | 5 | 4 | 5 |
| 3 | 4 | 3 | 4 | 3 | 4 | 5 | 4 |
| 2 | 3 | 2 | 3 | 4 | 3 | 4 | 5 |
| 3 | 2 | 3 | 2 | 3 | 4 | 3 | 4 |
| 2 | 1 | 4 | 3 | 2 | 3 | 4 | 5 |
| 3 | 4 | 1 | 2 | 3 | 4 | 3 | 4 |
| 0 | 3 | 2 | 3 | 2 | 3 | 4 | 5 |