Shapes as well as colours: block puzzles for colour-blind players

A block puzzle deals pieces in different colours, so it is fair to wonder what a player loses if some of those colours look the same. On a 9x9 board that clears rows, columns and 3x3 boxes, the answer is very little. A group clears when all nine of its cells are filled. What colour they are filled with does not enter into it.

How common colour vision deficiency is

Colour vision deficiency (often called colour blindness, though true absence of colour vision is rare) comes from one of the three types of cone cell in the retina working differently. The usual figures for people of Northern European descent are about 8% of men and about 0.5% of women. The gap exists because the genes for the red and green cones sit on the X chromosome: a man has one copy and a woman has two, so a fault is far more likely to show in a man.

Put as counts, that is roughly 1 man in 12 and 1 woman in 200. In a room of 1,000 men and 1,000 women, expect about 80 men and 5 women. Rates differ between populations, and these are the figures usually quoted for Northern Europeans.

The types, briefly

The names follow one pattern. The prefix says which cone is affected, and the ending says how badly.

• Protan types affect the red-sensitive cones. Protanomaly shifts their sensitivity, so reds look duller and darker; protanopia means they are missing.
• Deutan types affect the green-sensitive cones. Deuteranomaly is the most common of all, and deuteranopia is the missing-cone form.
• Tritan types affect the blue-sensitive cones. They are much rarer than red-green and mix up blues and greens, and yellows and violets.

Protan and deutan types together are the red-green group, which is where almost all of the 8% sits. The pairs that tend to blur are red and green, orange and green, brown and green, and pink and grey. A palette that leans on those pairs to tell pieces apart is the one that causes trouble.

Why the clearing rule makes colour optional

The board has 81 cells and 27 groups that can clear: 9 rows, 9 columns and 9 boxes. Each group is nine cells. The test for each is the same, and it has two outcomes: a cell is filled or it is empty. A row of nine blocks in nine different colours clears exactly as a row of nine in one colour does. Colour never decides whether a group is complete, how many cells it frees or what scores.

That is how the clearing is described for Big Ben Blocks: Block Puzzle: place pieces on a 9x9 grid and complete rows, columns or 3x3 boxes to clear space. The information a player needs from the board is where the filled cells are, and filled against empty is a difference in lightness and outline as much as in hue, which is the part colour vision deficiency leaves alone.

Reading a board by occupancy

Everything below uses only filled and empty, so it works however you see the colours.

1. Count the empty cells in a group, not the filled ones. A row with 2 empty cells is 7 of 9 done. Any group with 1 or 2 empty cells is a candidate to finish.
2. Check all three groups for a cell. Every cell sits in one row, one column and one box, as the post on the 27 groups counts. A gap whose row, column and box are all nearly full is worth the most.
3. Trace the shape of the gap. A gap of 3 cells in a line takes a straight piece of 3 and nothing else. Match the outline of the space to the outline of the piece.
4. Look for walled-in cells. An empty cell with no empty neighbour only takes a single block. The post on holes and islands has the counts.
5. Plan the double. Two groups that each need the same piece can clear together; the double-clear post sets out how.

None of those steps asks which colour a block is. You can check this yourself: on Android, the accessibility settings include a colour correction option and a greyscale filter, and playing a few boards under either is a quick way to see how much of the game survives without hue.

Where colour does still matter

Colour is not entirely idle. It can help a sighted player recognise a piece at a glance, and in a game with scoring goals tied to a particular colour it would matter more. For that reason it is useful when a game does not rely on colour alone. The Big Ben Blocks description says blocks carry shape symbols as well as colours, so each piece has a second cue beyond its hue. It also lists tap-to-place controls as an alternative to dragging, screen-reader labels and reduced-motion support. The listing does not say more than that about how any of these are built, so treat this post as describing the general idea, not a tour of the settings.

When you pick any block puzzle, two quick checks are worth making. First, does the board look readable in greyscale, with filled cells clearly different from empty ones? Second, is anything dependent on matching colours? If the answer to the second is no, as it is for a straightforward 9x9 clearing game, colour vision deficiency should not hold you back.