Showing posts with label cogs. Show all posts
Showing posts with label cogs. Show all posts

Saturday, August 20, 2011

How to move two aligned tile pieces to the top of a scheme in sliding puzzles?

Question

While playing Cogs, I have found myself plenty of times in this irritating situation. I have this:

.--. 
|XY| (where I don't really care about X, Y, or Z)
|AB|
|Z |
....

...while what I want is this:

.--. 
|AB| (where again, I'll sort X, Y and Z later.)
|XY|
|Z |
....

I'm tired of trying to get this by accident. By goodness, you how do you make that happen consistently?

Answer

.--.   .--.   .--.   .--.   .--.   .--.   .--.   .--.   .--.   .--. 
|XY| → |XY| → |XY| → |↓Y| → |Y←| → |YA| → |YA| → |↓A| → |A←| → |AB|
|AB| → |A↓| → |→A| → |XA| → |XA| → |XB| → |XB| → |YB| → |YB| → |Y↑|
|Z | → |ZB| → |ZB| → |ZB| → |ZB| → |Z↑| → |→Z| → |XZ| → |XZ| → |XZ|
....   ....   ....   ....   ....   ....   ....   ....   ....   ....

10 moves.