The mirror rule on a six-column grid is column 5 minus the source column, so source cells in column 0 map to column 5, column 1 maps to column 4, and column 2 maps to column 3. In this symmetry game, every right-half cell you paint must equal that mapping applied to one of the fixed left-half source cells, and finishing all five mirror sets adds up to exactly 1,000 points. The Symmetry Puzzle is a browser-based coordinate game played on a six-column by four-row grid with a vertical axis between columns two and three when columns are numbered zero through five. Every level reveals a fixed pattern on the left half, and your task is to paint the corresponding cells on the right half so the completed grid mirrors cleanly across that axis. The game does not infer symmetry from an uploaded image or run a vision model; it compares the cells you paint against a finite authored coordinate set that is fully disclosed. That disclosure is what separates this symmetry game from picture-mirror apps — every cell you click is verified against an exact target set, and every target set is independently audited before the game begins.
What the Symmetry Game Actually Asks You to Do
Each of the five levels in this symmetry game has the same structure. The left half (columns zero, one, and two) is treated as input and is already painted for you. The right half (columns three, four, and five) starts empty. You decide which cells to paint on the right half until the painted set exactly matches the disclosed mirror set for that level. As soon as equality is reached, the level advances, you earn 200 points, and the next pattern appears.
The five patterns use the following source-cell counts:
| Level | Source cells on the left half |
|---|---|
| 1 | 3 |
| 2 | 4 |
| 3 | 6 |
| 4 | 5 |
| 5 | 6 |
Across the five levels, the right half must receive the same number of mirror cells as the left half holds source cells: 3 + 4 + 6 + 5 + 6 = 24 source cells and therefore 24 target cells. No source cell is reused inside a level, and every target cell falls on the right half because the mirror formula always pushes coordinates outward from column two.
The Mirror Rule on a Six-Column Grid
The symmetry game replaces the column of every source cell using the formula mirrored column = 5 − source column, while keeping the row unchanged. The grid has six columns numbered zero through five, so the rule produces three symmetric pairs:
| Source column | Mirror column | Pair |
|---|---|---|
| 0 | 5 | 0 ↔ 5 |
| 1 | 4 | 1 ↔ 4 |
| 2 | 3 | 2 ↔ 3 |
The reverse pairs are identical, which means applying the rule twice returns you to the original column. As a worked example, take a source cell at row 2, column 1. The row stays at 2, and the mirror column is 5 − 1 = 4, so the target cell sits at row 2, column 4. Apply the rule again and column 4 returns to column 1, confirming the pair is its own inverse.
Because every source cell sits in columns zero, one, or two, the formula guarantees that every mirror cell lands in columns three, four, or five. That guarantee is what makes the symmetry game solvable on a six-column board: you never have to worry about a target falling back on the source side, and the right half is always wide enough to hold every required cell without overlap or overflow.
How to Read Each Fixed Pattern Before You Paint
Before painting anything, scan the left half of the current level. The left half is a three-column by four-row block containing a small abstract shape made of already-painted cells. Note the row of each painted cell and the column it sits in. The patterns are abstract coordinate fixtures rather than images, so you are not asked to recognize letters, logos, or photographs — every level is independent and every pattern is a fresh coordinate set.
The screen reports the level number, the number of source cells, the current painted count on the right half, the cursor position, the number of mistakes, and the current score. Use the source-cell counter as your checklist. If a level says "5 source cells," then exactly five mirror cells are required, and the level will not advance until your right-half painted set has five cells. If the painted counter stalls below the source-cell counter for several moves, re-check the column mapping on the cell you just painted before continuing.
How to Play a Level of the Symmetry Game
- Identify the first source cell on the left half and note its row and column. For example, a cell at row 0, column 2 has row 0 and column 2.
- Compute its mirror using column 5 minus the source column. For row 0, column 2, that gives 5 − 2 = 3, so the target is row 0, column 3.
- Move the cursor to that right-half cell using the Arrow keys, or click the cell with a pointer or touch screen. The cursor stays inside the right half.
- Press Space or Enter to paint the cell, or click it directly. Painting a required mirror cell adds it to the painted target set.
- Repeat for every remaining source cell, working through them one at a time until the source-cell counter matches the painted counter and the level advances.
- Continue through all five levels. Each completed mirror awards 200 points, and 5 levels × 200 points = 1,000 points for the full symmetry game.
If you paint a right-half cell that is not in the disclosed mirror set, you create one recoverable error. Painting an already-finished cell is a no-op. A second distinct wrong cell closes the run, so the symmetry game rewards careful one-by-one application of the rule over rapid guessing.
Scoring, Mistakes, and the Path to 1,000 Points
The symmetry game uses an exact-score contract rather than a continuous ranking. Each level is worth a fixed 200 points, awarded only when your right-half painted set exactly equals the disclosed mirror set. There are no partial awards for partially complete levels, so a half-finished level is worth zero points. With five levels at 200 points each, the maximum run totals 1,000 points. The score is shown live on the screen, but it only changes when a level actually advances.
Mistake handling is also transparent. The first time you paint a wrong right-half cell, the run continues and the screen reports one mistake. If you paint that exact same wrong cell again on the same level, the mistake count stays at one because the error signature is deduplicated by its level-row-column triple. The run only ends when you paint a second distinct wrong cell — a different row, a different column, or a different level from your first mistake. Source-side input, out-of-bounds positions, fractional coordinates, and unknown rows or columns are strict atomic no-ops, so they neither count as mistakes nor advance the level. Restart restores the first level, its fixed source pattern, an empty target half, zero score, and zero mistakes, and the symmetry game then begins again from the opening pattern.
Keyboard and Pointer Controls Compared
The symmetry game accepts both pointer and keyboard input on every right-half cell. With a mouse or touch screen, click any right-half cell to paint it. The screen reports the current cursor position even when you are using the pointer, which makes it easy to confirm where the next click will land before committing.
For keyboard players, the Arrow keys move a visible cursor within the right half. The cursor cannot cross into the fixed source half, so you don't have to guard against painting the wrong side. Once the cursor sits on the cell you want, press Space or Enter to paint it. Buttons and directional controls meet a 44-pixel target size, which keeps tap and key targets accessible on small screens and touch devices.
A useful habit is to plan the entire mirror set before moving the cursor at all, especially on level 3 and level 5 where the source cells number six. Sketch the row and column of every source cell, run each through column 5 minus source column, and verify the resulting target cells sit in columns three, four, and five. Then execute the plan cursor move by cursor move. The mirror rule is short, the coordinate sets are short, and the disclosed scoring means there is no benefit to guessing. For a deeper walkthrough of the exact coordinate sets and how each level is independently audited, see Complete the Symmetry: Mirror Five Patterns to 1,000. The full symmetry game itself is at the Symmetry Puzzle page.
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