MathDB

20 \times 20

treasure map is glued to a torus. A treasure is hidden in a cell of this map. We can ask questions about

1\times 4

4 \times 1

rectangles so that we find out if there is a treasure in this rectangle or not. The answers to all questions are absolutely true, but they are given only after all rectangles we want to ask are set. What is the least amount of questions needed to be asked so that we can be sure to find the treasure? (If you describe the position of the cells in a torus with numbers

(i, j)

of row and column,

1 \leq i, j \leq 20

, then two cells are neighbors, if and only if two of the coordinates they have are the same, and the other two differ by

1

mod

20

Problem Statement