Hi guzzlers
Today’s puzzle is for escapologists.
Imagine you are in a grid 100 squares long and 100 squares wide. (The grid is fixed to the compass directions: up/down is N/S, and left/right is W/E.) On each square of the grid, there’s an arrow. Each arrow is pointing either N, S, W or E.
Choose any square. That’s your starting position. Now the game begins.
The rules are that you must always follow the arrow. So, if the arrow in your starting square points N, you move to the square due north. If the arrow points E, you move to the square due east.
But there is an extra thing you need to do. Once you arrive in a new square, you must rotate the arrow in the square you came from by 90 degrees clockwise. So if the square you came from pointed N, then once you leave that square you must rotate that arrow to E. If the square you came from pointed E, once you leave that square you must rotate that arrow to S.
Safely in your new square, you repeat the process: follow the arrow to a new square, and then rotate the arrow in the square you came from by 90 degrees.
If you are in a square on the top edge and the arrow points north, then the following move you are going to get out the grid. Hurrah! You win! Likewise if you are on any of the other edge squares of the grid, and the arrow in the square points out, you get out.
But if you are not on an edge, you will probably start roaming around the grid. Here’s a statement:
“No matter which directions the arrows are pointing at the start, and no matter which square you choose to begin, you will always eventually get OUT OF THE GRID”
True or false? Prove it one way or the other.
I’ll be back at 5pm UK time with the answer.
The comments are open below, but please, NO SPOILERS!!!
Thanks to Juan Pablo Pinasco, of the University of Buenos Aires, and Adrian Paenza for suggesting today’s puzzle.
I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.
I’m the author of several books of popular maths, including the puzzle books Can You Solve My Problems? and Puzzle Ninja. I also co-write the children’s book series Football School.