Hard Difficulty

Square-1 The Puzzle That Changes Shape

The Square-1 is a completely unique twisty puzzle that literally changes shape as you solve it. Unlike cubic puzzles, the top and bottom layers can be twisted to create star, kite, and other irregular shapes. The first challenge is restoring the cube shape — only then can you solve the colors.

Pieces 21 (8 corner pieces, 8 edge pieces, 2 middle-layer halves, 1 equatorial divider, 2 middle wedges)

Permutations 552,738,816,000

God's Number Unknown

World Record 4.59s (Max Siauw)

Inventor Karel Hršel & Vojtech Kopský

Year 1990

Interactive 3D Square-1

Interactive 3D Square-1 Solver — scramble the puzzle and watch the step-by-step solution.

Loading 3D Model...

Camera Angle:

Solver Engine

Scramble Move Sequence

Solution

Step-by-Step Mode Step 0 / 0

Speed

Click Play or Next to start learning the moves!

Controls

History & Background

Invented by Karel Hršel and Vojtech Kopský in Czechoslovakia in 1990. Originally called "Cube 21" or "Back to Square One" — the name reflects the goal of returning it to its square shape. It became a WCA competition event and has developed a dedicated speedcubing community.

Notation Guide

Square-1 uses a unique (x, y) / notation system. x and y represent 30° increments for the top and bottom layer turns. The / symbol means "slice" — flipping the right half 180°.

(x, y) Turn top layer x×30° CW, then bottom layer y×30° CW

/ Slice — flip the right half 180°

(1, 0) Turn top 30° clockwise, bottom stays

(0, -1) Top stays, bottom turns 30° counter-clockwise

(-2, 3) Top 60° CCW, bottom 90° CW

Visual Guide & Cheat Sheet

A complete visual guide illustrating the puzzle's structure, standard layer movements, and key solving stages.

Step-by-Step Solving Guide

Step 1: Cube Shape

The most critical and unique step! Restore the puzzle from its random shape back into a perfect cube. You need to understand which pieces are "corners" (large, take 2 clicks of space) and which are "edges" (small, take 1 click). Arrange them so each layer has exactly 4 corners and 4 edges alternating.


                                                Various shape-specific algorithms

Learn to count "clicks" — each 30° turn is one click. Corners occupy 2 clicks, edges occupy 1 click. Each layer totals 12 clicks.

Step 2: Corner Orientation (CO)

Fix the corners so that the correct colors face up and down. At this point, the puzzle is cube-shaped and you work on getting white and yellow (or your chosen colors) on top and bottom faces.


                                                / (3, 3) / (-3, -3) /

There are only a few CO cases to learn. Identify them by counting the number of correctly oriented corners on each layer.

Step 3: Edge Orientation (EO)

Orient the edges so their top and bottom stickers match the top and bottom face colors. This step preserves the corner orientation from Step 2.


                                                / (3, -3) / (-3, 3) /

EO algorithms are designed to preserve CO. Practice them in isolation before combining with other steps.

Step 4: Corner Permutation (CP)

Place all 8 corners into their correct positions around the cube. The edges may still be wrong after this step — that's expected.


                                                / (3, 3) / (-1, -1) / (-4, 2) /

Learn to recognize which corners are already in the correct position to choose the right algorithm.

Step 5: Edge Permutation (EP)

The final step — cycle all edges into their correct positions. Some EP cases may also require a parity fix, which swaps 2 edges that couldn't otherwise be exchanged.


                                                / (3, -3) / (0, 3) / (-3, 0) / (3, -3) /

The parity algorithm is needed when an odd number of edge swaps are required. Learn it alongside your EP algorithms.

Key Algorithms

Name	Algorithm	Use Case
Cube Shape (Star)	`/ (-2, 4) / (4, -2) /`	Restore cube from star shape
Adjacent Corner Swap	`/ (3, 3) / (-1, -1) / (-4, 2) /`	Swap two adjacent corners
Diagonal Corner Swap	`/ (3, 3) / (0, -3) / (0, 3) / (-3, 0) /`	Swap two diagonal corners
Edge 3-Cycle	`/ (3, -3) / (0, 3) / (-3, 0) / (3, -3) /`	Cycle 3 edges
Parity	`/ (3, 3) / (1, 0) / (-2, -2) / (2, 0) / (2, 2) / (-1, 0) / (-3, -3) /`	Fix Square-1 parity

Common Mistakes to Avoid

Forcing moves when the puzzle layers aren't aligned — make sure both layers are flush before attempting a slice (/).

Confusing corners and edges after the cube is scrambled into a non-cube shape — corners are always larger (2 clicks wide).

Not counting clicks correctly — an off-by-one error prevents the slice from working and can break the cube shape.

Applying the wrong shape algorithm — there are dozens of shape cases. Use a reference chart until you recognize them naturally.

Frequently Asked Questions

Why does the Square-1 change shape?

Unlike standard cubes where all pieces are the same angular size, Square-1 corners are twice as wide as edges (2 clicks vs 1 click). When you twist layers by arbitrary amounts, the unequal piece sizes create irregular, non-cubic shapes.

Is the Square-1 notation hard to learn?

It's different but logical. The (x,y) / system counts 30° increments for top (x) and bottom (y), and / means slice the right half. Most people adapt within a few practice sessions.

What is Square-1 parity?

Square-1 parity occurs when the edges are in a state that requires an odd number of swaps — impossible with standard EP algorithms alone. A dedicated parity algorithm temporarily disrupts and restores the cube to resolve it.

Do I need to know a 3×3 first?

Not necessarily! The Square-1 is a completely independent puzzle with its own notation, algorithms, and solving method. However, general cubing experience helps with spatial reasoning.

Pro Tips & Tricks

The Square-1 notation system (x,y) / is completely different from standard cube notation. Take time to understand it before memorizing algorithms.
Cube shape is the hardest step for beginners. Practice restoring shape from random scrambles repeatedly until it becomes intuitive.
Learn to "count clicks" — top and bottom layers have 12 clicks each. Corners = 2 clicks, edges = 1 click. This is essential for shape restoration.
The Vandenbergh method (CSP: Cubeshape → CO → EO → CP → EP) is the most popular speedsolving approach.
The QiYi Square-1 Pro M and MoYu RS Square-1 M are popular and affordable speedcubes.
Parity on the Square-1 is fundamentally different from NxN parity — it's a unique state caused by the shape-shifting mechanism.

Try Our 3×3 Solver

Interactive 3D solver with step-by-step animations

Launch Solver