A boggling puzzle?

Question

A heavy armchair is currently on a black tile on the floor. You want to move it so it is on the adjacent white tile, facing the same way. It is so heavy that you can only move it by swiveling it by 90 degrees around one of its corners. Is it possible to make the move?

Answer 1

It isn't possible. It takes an odd number of rotations to reach one square away. To see this, start by moving it to the right square in one move. Now for every square you move in any direction you'll have to move it a square back in the opposite direction to get back to the right square. To get the chair facing the right direction you need to rotate it some multiple of 4 times. 4 rotations is even but you can only reach the right square in an odd number of moves.

Answer 2

Nope, its not possible. Each move takes you to the other color tile and rotates you 90 degrees. Starting on a black tile, your first move takes you to a white tile. Your next move takes you to a black tile. Extending this, after an even number of moves you are on a black tile. After an odd number you are on a white tile.

To be facing the same way, you must have rotated an even number of times. If you start out facing north then after one move you are facing east or west. One more move and you are facing north or south. Continue this and you wil see that if you take an odd number of moves you are facing east or west. After any even number of moves, you are facing north or south.

So to face the same way as you started takes and even number of moves but to be on a white tile takes an odd number. Therefore you can't be facing the same way on any white tile.

Answer 3

Yes! you can move it in a 90 degree angle. But if you tried moving it at a 180 or a 270 degree angle it would be hard maybe impossible.

Answer 4

Of course.. movers regularly 'walk' refrigerators into correct position in the kitchen by swiveling it on one corner and then the next.

Answer 5

Yes definitely it can be moved. Your question has the answer.