Square-1 (puzzle)

Its distinguishing feature among the numerous Rubik's Cube variants is that it can change shape as it is twisted, due to the way it is cut, thus adding an extra level of challenge and difficulty.

The Super Square One has two additional layers that can be scrambled and solved independently of the rest of the puzzle, and the Square Two has extra cuts made to the top and bottom layer, making the edge and corner wedges the same size.

The Square-1 (full name "Back to Square One") or alternatively, "Cube 21", was invented by Karel Hršel and Vojtěch Kopský in 1990.

The middle layer contains two trapezoid pieces, which together may form an irregular hexagon or a square.

In its solved (or original) state, viewing the cube from the face with the word "Square-1" printed on it, the colors are: white on top, green on the bottom, yellow in front, red on the left, orange on the right, and blue behind.

Although these solutions use different approaches, most of them try to restore the cube shape of the puzzle first, regardless of the placement of the pieces and the parity of the middle layer, and then proceed to put the pieces in their correct places while preserving the cube shape.

These are sequences of turns and twists that will rearrange a small number of pieces while leaving the rest of the puzzle untouched.

However, while solutions of the Rubik's Cube rely on these algorithms more towards the end, they are heavily used throughout the course of solving the Square-1.

[2] The original Square-1 notation was created by Jaap Scherphuis: A slash (/) indicates turning the entire right half of the puzzle by 180°.

It is based on the original notation, with brackets and slashes being removed, with the latter being replaced with spaces, and with letters being assigned to common move sets.

This notation was proposed as an easier way to write, learn and share speedsolving algorithms.

The full notation is here, but this is an abridged version:[3] The world record for single solve is 3.41 seconds, set by Ryan Pilat of the United States at Wichita Family ArtVenture 2024.

It consists of 4 layers of 8 pieces, each surrounding a circular column which can be rotated along a perpendicular axis.

The "Square Two" is yet another variation of the popular Square-1 puzzle, with extra cuts on the top and bottom layers.

This removes the locking issue present on the Square-1, which in many ways makes the Square Two easier to solve (and scramble) than its predecessor.

In many ways, it's actually easier considering one can always make a slice turn regardless of the positions of the top and bottom layers.

Mostly, it's solved just like the Original, merely requiring the extra step of combining the corner wedges.