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I haven't downloaded the app, so maybe this makes sense somehow, but the following text from the app description confused me:

Difficulty ratings:

- 2x2 board - Easy

- 3x3 board - Easy

- 4x4 board - Hard

- 5x5 board - Medium

- 6x6 board - Impossible

- 7x7 board - Hard

Shouldn't the difficulty rating increase with increasing board size?

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Solving an even square might be inherently harder than an odd square. I haven't played the game though.

Yep, it requires n^2 moves for even boards while odd boards require less moves (no formula found yet). Using a computer, I found, by brute force, that the 5x5 can be solved in 8 moves at most, the problem quickly becomes intractable for 7x7 and above. It looks like this might be NP hard according to another post: http://stackoverflow.com/questions/27436275/how-can-i-furthe...

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