Optional Lab · Ages 10–16
The Thinking Cube
From a Rubik's cube to code — a live bridge between Mathematics, Algorithms and Coding.
Possible states
43 × 10¹⁸
43,252,003,274,489,856,000
God's Number
≤ 20
moves to solve any cube
Moving pieces
26
6 centers · 12 edges · 8 corners
Stickers
54
6 faces × 9 tiles
U UpR RightF FrontD DownL LeftB Back
Modifier
Faces
Move tape
Length: 0≤ God's Number (20)
Tap a face to start. Try R U R' U' — the famous "Sexy Move".
The Three Bridges — live
Every move is narrated as Mathematics, an Algorithm step, and Scratch-style code.
M
Mathematics
Each move rotates a face 90° around a fixed axis. 6 faces × 3 turns = 18 quarter/half turns.
A
Algorithm
A cube algorithm is an ordered list of moves. Order matters — swap two and the outcome changes.
C
Code
In Scratch: add each move to a list, then repeat through the list to replay it.
Possible sequences of this length1= 18^n · a small algorithm beats brute force.
Try these challenges
1
The Sexy Move
Build R U R' U' then apply it 6 times. What happens? Why?
2
Undo, precisely
Scramble the cube, then hit Reverse. The inverse of A·B·C is C'·B'·A'.
3
Cycle of four
Add R four times. The face returns to its start — a cycle of length 4.
Reasonix MAC™ · Optional labs are for exploration — no grades, real thinking.