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**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

http://www.mathsisfun.com/games/orientation-puzzle.html

MathsIsFun says its: Tricky! (I predict you will be using undo a lot). I dont fully agree. You just need to work backwards! Take the Level-10 puzzle, for instance:

In order to solve it you need to arrive at the gate in the facing-down position.

In order to arrive at the gate in the facing-down position, you need to rotate counterclockwise from the facing-left position at the gate. (There is no other way.)

In order to arrive at the gate in the facing-left position, you need to move up from square #7 (numbering the squares #116 left to right from top to bottom) in the facing-left position.

In order to arrive at square #7 in the facing-left position, you need to move left from square #8 in the facing-left position.

In order to arrive at square #8 in the facing-left position, you need to rotate clockwise from the facing-down position at square #8.

And so on.

You just need a bit of lateral thinking to help you with the solution.

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

I agree partially, but it doesn't make the problem simple. For a start, it takes a lot longer to work out your route going backwards, and it's very possible that you could solve the maze quicker just by trying stuff and undoing a lot, rather than by analysing it. That could well be the intended method of solving.

Also, even with the patience to work it all through, it's still not completely foolproof. Continuing the backwards route gets you to a point where you need to be in square #2, facing right.

However, you can get to that square from either #1 or #6, so working backwards doesn't eliminate all branches, it just reduces them a lot.

I actually prefer working forwards, because although there are more branches, it's far easier to think about it, and most of the branches prove themselves to be dead ends (or loops back to an earlier section of path) within a few turns anyway, so you'll never be going along the wrong route for too long.

Perhaps the best method would be to somehow combine the two routes and meet somewhere in the middle.

Why did the vector cross the road?

It wanted to be normal.

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