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Knight to the centre

BrainteasersEasy

A knight stands on a corner square of a $5$ by $5$ board. It moves like a chess knight: $2$ squares in one direction and then $1$ square at a right angle to it. What is the minimum number of moves needed to reach the centre square of the board?

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Hint

A knight changes the colour of its square on every move. Which squares can it reach in $2$ moves?

Solution

Colour the board like a chessboard. The corner and the centre have the same colour, and a knight changes colour with every move, so the number of moves is even.
Number rows and columns from $1$ to $5$ , so the corner is $(1, 1)$ and the centre is $(3, 3)$ . In $2$ moves the knight can reach only $(1, 1)$ , $(3, 1)$ , $(1, 3)$ , $(2, 4)$ , $(4, 2)$ , $(4, 4)$ , $(5, 1)$ , $(1, 5)$ , $(3, 5)$ , $(5, 3)$ , and the centre is not among them.
In $4$ moves the knight reaches the centre: $(1, 1)$ , $(2, 3)$ , $(3, 5)$ , $(5, 4)$ , $(3, 3)$ .
The minimum number of moves is $4$ .

Answer: $4$

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