Question 43
All numbers from $1$ to $16$ are written in a $4 \times 4$ board, one in each cell. We calculate all the differences between two numbers that occupy adjacent cells and call *value* of the board the greatest of these differences.
Which is the smallest value that a board can have?
Show a board having that value and explain why no board can have a smaller value.
*Remark:* Two cells are adjacent if they share a side.
*Remark:* The difference between two numbers is the subtraction of the smaller from the larger of them.
Which is the smallest value that a board can have?
Show a board having that value and explain why no board can have a smaller value.
*Remark:* Two cells are adjacent if they share a side.
*Remark:* The difference between two numbers is the subtraction of the smaller from the larger of them.