Note: To improve the turning experience, we programmed the Square-1 so that it cannot get "locked". This means that each turn of the top or bottom layers will end at the next "unlocked" position. Pay attention to this as you try out different algorithms :)
The Square-1 (a.k.a. SQ1, Cube 21 or Back to Square One) is a cube-shaped shape-shifting twisty puzzle. It was invented by Karel Hršel and Vojtěch Kopský in 1990 and was approved as a Czechoslovak patent in October 1992. It was initially mass-produced by Irwin Toy in the early 1990s; however, today many companies produce and sell it and its variations, most notably the Square-2 and Square-0.
The Square-1 is constructed of 3 layers of parts. The top and bottom layers have 4 kite-shaped corner pieces and 4 triangular edge pieces each. The middle layer contains only 2 trapesoid pieces, which together can form either a square or an irregular hexagon. An interesting fact to note about this puzzle's mechanism is that the corner and edge pieces are interchangeable and can occupy each other's places. Both types of pieces are anchored to the center of the cube and are radially symmetric. The difference is that the corner pieces span 60° out from the center, while the edge pieces only span 30° out. This fact allows two adjacent edge pieces to be replaced by a single corner piece and vice versa. That means that when scrambling this puzzle, you can get 6 of the corner pieces to all occupy the same layer in a delightful flower shape. We invite you to give it a try!
Thanks to this interchangability of the corners and edges, the Square-1 has a relatively high number of possible combinations: 11,958,666,854,400 to be exact! This is especially impressive considering the puzzle only has 18 parts. Compare that, for example, to the Redi Cube, which has 20 moving parts but only about 12% of the possible combinations. Computer simulations show us that each of the Square-1's possible combinations can be solved in 31 moves or less.
The Square-1 is the ONLY shape-shifting official WCA event. The current world record for solving it is 3.73 seconds, set by Ryan Pilat at the CubingUSA Heartland Championship 2023.