One of our first iPhone puzzles – Brain Twister published quite long time ago still gets downloads. BTW it’s a free puzzle game for iPhone so download it from iPhone AppStore and check it out yourself. Brain twister is very hard puzzle game which should be solved in 40 steps.
We’d like to help our customers in solving it, so this post will explain you how to solve Brain Twister exactly in 40 steps. It’s easier than you though!
The first thing we do to understand Brain Twister’s mathematical justification is numbering its game field. Let’s enumerate each circle on the game field:
Then we should determine all possible moves for each ball, keeping in mind that it only can be moved as knight’s move in chess. We will skip step where we created transition matrix, it’s not essential here. When you got all possible moves for each ball, you can draw a transition graph – it’s more important to understand Brain Twister mathematics. The graph itself will look like this one:
Now we can see that transitions graph has a “bottleneck” – circle number 4. In fact we need to rearrange green balls and red balls, all of them will be passed through circle number 4.
Our first step is to put green ball from position number 1 to position number 8, and red balls on 2 and 10, then we can easily move green ball from position 6 to position 5 and forget it – it’s in a final place for this ball.
Then we move red balls on positions 7 and 1, then we can move green ball from position 8 to position 6. Now to put green ball from position 6 to position 7 we need to lift red balls back to 2 and 10.
OK, now bottleneck is free and we easily pass green ball from position 6 to position 7. All we need to do now – put the red balls into the red circles!
If you done things right – you will complete it in 40 moves!
Congratulations, the goal is completed! Was it difficult? :)
BTW, there is at least one more way to do it in 40 moves.
