Mathematical Reference

The Canonical 7-Segment Matchstick Matrix

Every puzzle in Move 1 Stick models numerals after classical electronic seven-segment LED displays. Understanding the precise segment geometry, bitmask encoding, and single-stick permutations is the fastest way to recognize candidate moves without guesswork.

Display Anatomy

Segment Anatomy & Bitmask Layout

Each digital digit resides in an indexed 7-slot matrix. In our procedural engine, these segments are tracked as binary flags from index 0 to index 6:

       ── 0 ──
      │       │
      1       2
      │       │
       ── 3 ──
      │       │
      4       5
      │       │
       ── 6 ──
  Index Mapping:
  0: Top            1: Top-Left       2: Top-Right
  3: Middle         4: Bottom-Left    5: Bottom-Right
  6: Bottom

A bitmask integer is formed by shifting active segments. When a stick is moved, the solver verifies the updated bitmask against our static lookup table (DIGIT_BY_CODE). If the resulting pattern does not correspond to a valid digit between 0 and 9, the move is rejected.

Cheat Sheet

The Master Single-Stick Mutation Table

The table below lists all single-stick transformations possible for every digit. In any valid move, you either donate a stick (−1), receive a stick (+1), or transpose a stick within the same glyph (internal shift).

Digit	Binary Bitmask	Active Sticks	Add 1 Stick (+1)	Remove 1 Stick (−1)	Shift 1 Stick (Internal)
0	`[1,1,1,0,1,1,1]`	6	Becomes 8 (adds slot 3)	—	Becomes 6 or 9
1	`[0,0,1,0,0,1,0]`	2	Becomes 7 (adds slot 0)	—	—
2	`[1,0,1,1,1,0,1]`	5	—	—	Becomes 3 (moves 4 to 5)
3	`[1,0,1,1,0,1,1]`	5	Becomes 9 (adds slot 1)	—	Becomes 2 or 5
4	`[0,1,1,1,0,1,0]`	4	—	—	—
5	`[1,1,0,1,0,1,1]`	5	Becomes 6 or 9	—	Becomes 3 (moves 1 to 2)
6	`[1,1,0,1,1,1,1]`	6	Becomes 8 (adds slot 2)	Becomes 5 (loses slot 4)	Becomes 0 or 9
7	`[1,0,1,0,0,1,0]`	3	—	Becomes 1 (loses slot 0)	—
8	`[1,1,1,1,1,1,1]`	7	—	Becomes 0, 6, or 9	—
9	`[1,1,1,1,0,1,1]`	6	Becomes 8 (adds slot 4)	Becomes 3 or 5	Becomes 0 or 6

Operator Mechanics

Operator Glyphs & Symbol Rules

Matchsticks are not limited to numbers; mathematical symbols participate in transformations as well:

+ / −

Addition and Subtraction

A plus sign (+) consists of 2 matchsticks (horizontal and vertical). A minus sign (−) consists of 1 horizontal stick. Lifting the vertical match transforms + into −, yielding a spare stick for other terms. Donating a stick to − converts it into +.

The Equals Sign Anchor

The equals sign (=) is built from two parallel horizontal sticks. In standard game rules, the equals sign is immutable; matchsticks cannot be extracted from or added to it, ensuring a stable boundary between sides.

Engine Parser

Forbidden Shapes & Evaluation Constraints

When formulating solutions, the validation parser enforces three strict constraints:

No Incomplete Glyphs: Creating a pattern not found in standard 7-segment encoding causes an immediate board shake and auto-returns the stick.
No Leading Zeros: Multi-digit numbers cannot start with zero (e.g. 06, 042). A single standalone 0 is valid.
Strict Operator Grammar: Operators cannot appear consecutively (e.g. ++ or +−) or sit at the immediate beginning or end of an equation.

Put the Matrix into Action

Now that you know every valid digit transition, learn how to spot these opportunities under time pressure.

Read 5 Pro Tips → Launch Puzzle Arena →