Question

A knight moves on a chessboard two squares up, down, left, or right followedby one square in one of the two directions perpendicular to the first part of the move (i.e.,the move is L-shaped). Suppose the knight is on an unbounded board at square (0,0) and wewish to move it to square (x,y) in the smallest number of moves. (For example, to move from(0,0) to (1,1) requires two moves. The knight can move to board locations with negativecoordinates.)

Answer 1

Answer:

Explanation:

Check attachment for solution.

Generally the movement of the knight is L, i.e (2,1), (1,2),(-1,2),(1,-2) etc.

So using Pythagoras theorem

x^2+y^2=1^2+2^2

x^2+y^2=5

Then, the knight will make one movement when the displacement is √5.

So let take a look at other positions

(1,0),(0,1),(-1,0), (0,-1).

Then, for us to have this kind of movement, the knight has to make 3 movements.

When the displacement is 1, then it will make 3 movement.

Let examine other positions

(2,2) or(-2,-2) or (2,-2) or (-2,2)

When the displacement is √8

Then, the movement of the knight is 4.

Let examine other points

(2,0) or (0,2) or (-2,0) or (0,-2)

When the displacement is 2.

The knight make 2 movement