3D Medusa
3D Medusa is simple colouring grown up. Instead of colouring one digit, it colours strong links across every digit at once — hence "3D", the third dimension being the digit itself. Two colours propagate through the grid, and wherever they collide you have found a contradiction that resolves a whole cluster of cells in a single stroke.
The idea
Start on any bi-value cell (two candidates) or any bi-location unit (a digit with only two homes). Give one option colour A and its partner colour B, then spread the colours along every strong link you can reach: a bi-value cell links its two digits, and a conjugate pair links the same digit in two cells. Because you follow all digits together, the web grows fast. Then hunt for a clash. If one cell ends up with two candidates of the same colour, that colour is false, so every B-coloured (opposite) candidate is true. If a single unit holds the same digit twice in one colour, again that colour is false. Even without an outright clash, any uncoloured candidate that sees an A and a B of its own digit can be removed.
A worked example
Colour a bi-value {3,7} cell in r1c1: its 3 becomes A, its 7 becomes B. Following conjugate pairs across the web, a 3 in r4c4 picks up colour B. Now the uncoloured cell r1c4 can see a 3 in colour A (r1c1, along row 1) and a 3 in colour B (r4c4, down column 4) — it sees both parities of the digit, so its own 3 is impossible and comes off. If instead two A-coloured 3s had landed in the same unit, colour A would be false outright, and every B candidate across the whole web would be confirmed at once.
A Medusa web seeded on a bivalue cell colours candidates A (green) and B (red) across digits. A 3 is green in r1c1 and red in r4c4; the uncoloured r1c4 sees the green 3 along row 1 and the red 3 down column 4 — both parities — so its 3 is removed.
Step by step
- Seed the colouring on a bi-value cell or conjugate pair.
- Propagate both colours along strong links across all digits.
- Look for a same-colour clash in a cell or a unit — that colour is false.
- Sweep uncoloured cells that see both colours of their digit and remove them.
Common mistakes
- Colouring weak links. Medusa spreads only along strong links; a shared unit alone is not enough.
- Mixing digits in a cell wrongly. A bi-value cell links its two different digits — keep track of which colour sits on which digit.
- Stopping too early. The power comes from a large web; extend the colouring as far as it will go before judging.
Which Sudoku types is this best for?
The same logic applies across variants, but it pays off more in some than others.