Question 14
On a $ 45 \times 45 $ square grid there is an echidna. From any cell, the echidna can move to any other cell that shares a side. The echidna makes a sequence of 2024 moves, after which it has visited each cell exactly once. Prove that it is possible to write the numbers from 1 to 2025, one in each cell, in such a way that:
• For any pair of adjacent cells in the same row, the cell containing the larger number was visited earlier.
- For any pair of adjacent cells in the same column, the cell containing the larger number was visited later.
• For any pair of adjacent cells in the same row, the cell containing the larger number was visited earlier.
- For any pair of adjacent cells in the same column, the cell containing the larger number was visited later.