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How to solve Twist: parity, the corner rule and the 15-twist grid

Eigengames team · 6 October 2026 · 5 min read

▶ Play Twist🎯 Try a grid with a corner already home

Seven tiles home. Only the 1 and the 2 are the wrong way round, side by side in the top row. It looks like one twist from finished. It’s nine. Not “about nine”, and not nine if you’re clumsy: our solver checked every possible grid, and that position needs nine twists at the very least.

Once you see why, Twist gets a lot less mysterious.

Every twist is three swaps

A twist moves four tiles one step round a little square. If you write that move as swaps of two tiles, it takes three of them. Mathematicians call that an odd permutation, and the key fact is that odd and even never mix. Every twist turns an even arrangement into an odd one and back again.

The goal grid is even (zero swaps from itself). So a grid that is an odd number of swaps away from the goal needs an odd number of twists, and an even one needs an even number. We checked this against the solver’s distance for all 362,880 numbered grids, and it holds for every single one. Easy mode is different: its tiles come in three identical colours, so swapping two same-coloured tiles changes nothing you can see, and parity tells you nothing.

That’s why the swapped 1 and 2 hurt. One swap is odd, so the answer is odd, and one twist can’t do it because a twist moves four tiles. The solver says the cheapest odd number that works is 9. Across all 36 ways to swap one pair of tiles, every one needs 9 or 11 twists. Three tiles cycled round need between 8 and 12.

The lesson for play is simple. Never aim for “almost solved”. A grid with two tiles swapped looks close and is anything but. It is usually much cheaper to leave several tiles slightly wrong and let one rotor fix them together.

A corner is touched by one rotor only

Look at which rotors can move each cell. A corner sits under exactly one rotor, an edge under two, and the centre under all four.

That’s where the corner rule on the game page comes from, and it’s correct. Once the right tile sits in a corner, stop using that corner’s rotor. The other three rotors never touch it, and we confirmed that between them they can reach all 40,320 arrangements of the remaining eight tiles. The worst of those takes 14 twists. Two rotors aren’t enough: the two bottom rotors on their own reach only 120 of the 720 ways the six lower tiles can sit, so finishing the top row first and then working with the bottom two rotors alone usually traps you.

Which corner first

The rule works, but it can cost you a lot if you pick the wrong corner. We tried it on 1,000 Normal puzzles. In each one we placed a corner tile in the fewest twists possible, then let the solver finish perfectly with the other three rotors.

So never fix the top-left out of habit. On 47% of Normal puzzles at least one corner tile already starts in place, and that corner costs nothing. Check all four corners before your first twist. If one is home, freeze its rotor and play with the other three. If two are home, pick the one that leaves the tiles around the other three rotors closest to right.

A second habit helps here. Two twists of the same rotor swap its tiles diagonally, top-left with bottom-right and top-right with bottom-left. When the tiles you need are diagonal from where they belong under one rotor, that’s your move.

The hardest grid has a solved middle

The farthest any numbered grid can be from the goal is 15 twists. Exactly one grid out of 362,880 needs all 15:

7 2 1
4 5 6
9 8 3

It looks friendly. The whole middle row is in place, and so is the 2. But every corner tile is in the wrong corner, so all four rotors have work to do, and the tiles that look finished have to move out of the way and come back. Just 14 grids need 14. The most common distance by far is 10 twists, about a third of all grids. That’s why Hard, with its par of 10 to 12, is still a typical scramble rather than a freak.

Practice

The practice puzzle is a Normal grid with tile 1 already in the top-left corner. Par is 7, and there’s a par route that never touches the top-left rotor at all:

Cover the figure and try to find it yourself first. Freeze the corner, count the twists, and remember that a pair of swapped tiles is never “nearly there”.

Fix a corner, freeze its rotor, and let parity tell you whether you’re close.

▶ Play Twist🎯 Try a grid with a corner already home