A rook has traversed the chessboard, visiting each square at least once. What is the minimum number of turns it could have made

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Either the rook made at least one move in each row, or it made at least one move in each column.

## Solution

An example with 14 turns is shown in the picture. Let's prove that there could not have been fewer than 14 turns. We will show that either the rook made at least one move in each row, or it made at least one move in each column. Indeed, if this were not the case, then the rook would not have made a single move in some row and in some column. But then the rook could not have visited the cell at the intersection of these row and column (the rook could neither enter this cell nor leave this cell). Therefore, we will assume that the rook made a move in each column. But between two moves in different columns, the rook must make at least 2 turns. Since there are 8 columns, there are at least seven transitions from one column to another, and the number of turns should be no less than $2 * 7=14$.

## Answer

14.00