Knight Teleportation Power!
It is known that a knight moves to a square that is two squares away horizontally and one square vertically, or two squares vertically and one square horizontally, which resembles the L-shape.
Suppose that for each of the four 8-by-8 chessboard edges, we include a portal, where it can teleport a knight from one side to the opposite. As shown to the right, a knight at position g7 can be teleported to a6 , a8 , f1 , or h1 --the squares that are impossible to reach without the portals. We can teleport the knight as long as its initial position is either a square away from or tangent to the closest edge.
Now, consider the puzzle, where two knights are at the opposite corners, as shown below. If we move the white knight in the same manner from the start (i.e. two squares left and a square up), is it possible to capture the black knight?
Note:
A knight can pass through two portals in a single move.
Bonus: Is it possible for the black knight to be captured on an -by- chessboard, where is an integer?
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
To capture the black knight, two things must happen at the same time, and I'm going to prove those can't happen at the same time: - The knight lands on a white square - The knight lands on an even row
The white knight starts on a white square, and with every move it has to move to a square of a different color. So we can deduce the knight must make some even amount of moves to land on a white square again.
But after some even amount of moves, the knight will always end up on a row with an odd number. So it's impossible for both of the conditions mentioned at the top to be true at the same time. Therefore the white knight can never capture the black knight.