3D Medusa colors candidates instead of cells. It joins the only two places of a digit in a house, as simple coloring does, and also the two candidates of a cell that has only two. The cluster gets two colors, and one of them is true everywhere. A color that turns up twice in a cell, or twice for a digit in a house, is false.
How to spot it
3D Medusa uses two kinds of strong link. One joins two cells, when a row, column or box has only two places for a digit. The other sits inside a cell with only two candidates. Simple coloring uses only the first kind, so it stays on one digit.
Color a candidate in a cell with two candidates blue. Give the far end of each of its strong links purple, and keep going until no link is left. Inside a cell the color jumps to the other digit, so the cluster can run from 2s to 6s to 1s and back. Then check it against the color rules below.
Color one candidate blue
Row one, column three has only a 2 and a 6. Color the 2 blue. The cell holds one of the two, so its 6 is purple.
Follow the 6 down column three
Column three has only two places for a 6, rows one and three. They take opposite colors, so the 6 in row three, column three is blue. That cell has only a 6 and a 1, so its 1 is purple.
Cross row three
Row three has only two places for a 1, in columns three and six. So the 1 in row three, column six is blue. That cell has only a 1 and an 8, so its 8 is purple.
Go up column six and along row one
Column six has only two places for an 8, rows one and three, so the 8 in row one, column six is blue. Row one has only two places for an 8, so the 8 in row one, column eight is purple. That cell has only a 2 and an 8, so its 2 is blue.
Blue meets itself in row one
Row one now holds two blue 2s, in columns three and eight. A row holds the 2 only once, so blue is false and purple is true. Strike all five blue candidates.
Why one color is true
Every link joins two candidates where exactly one is true. So if the blue 2 in row one, column three is true, the purple 6 beside it is false, the blue 6 below it is true, and so on round the cluster. If that 2 is false, everything flips. One color is true everywhere and the other nowhere.
The three color rules
The in-game hint uses three rules.
- A color twice in one cell. A cell can't be two digits, so that color is false. Simple coloring never meets this, since it stays on one digit.
- A color twice in one house. The same digit twice in one color in a row, column or box makes that color false. This rule fires here.
- A candidate that sees both colors. A candidate outside the cluster that shares a house with a blue and a purple copy of its digit is false, whichever color wins.
The first two remove a whole color. The third works even when no color clashes, and the quiz uses it.
What 3D adds to simple coloring
Try simple coloring on the 2 here. Column three has only two places for a 2, rows one and two, and no other link on the 2 touches them. Row one, column eight never gets a color, so the clash stays hidden.
3D Medusa gets there by changing digit. The color leaves row one, column three on the 6, travels on the 1 and the 8, and comes back on the 2. Each of the four links inside cells is where the digit changes.
Nothing up to simple coloring removes a candidate on this grid. XY-chains and AICs would, but the in-game hint tries 3D Medusa first, straight after simple coloring.
On the 2 alone, the chain ends at row two, column three. Row one, column eight gets no color.
Through the 6, the 1 and the 8, the color returns to row one on the 2, and the clash shows.
After the strike
Each of the five cells keeps one candidate: a 6, a 1, an 8, a 4 and an 8, as in the solution.
The in-game hint colors the whole cluster, 24 candidates here, and strikes 13 blue ones from 12 cells. You don't need all of it. Nine candidates prove that blue is false, and the singles do the rest.
Start in a cell with two candidates and switch colors at every strong link, between cells or inside one. If a color shows up twice in a cell, or twice for a digit in a house, strike it. Otherwise strike any candidate that sees both colors of its digit.
Where this sits on the path
3D Medusa removes candidates and leaves the placing to the singles.
It belongs to the chapter on chains and coloring, which simple coloring opens on one digit. The AIC mixes links between cells and inside cells in one chain. 3D Medusa uses the same two kinds of strong link, but grows a cluster and judges it by color.
X-cycles come next. Later in the chapter, Nishio tests one candidate instead of a whole color and checks it with the singles alone.
This board colors another part of the same cluster. It runs from the blue 2 in row one, column eight to row two, column three, whose 2 is purple, and no color meets itself in it. Which 2s can you strike?
Look for a 2 outside the cluster that shares a house with a blue 2 and with a purple 2.
Recap
- Look for
- Cells with only two candidates next to houses with only two places for a digit, joined into one cluster.
- Scope
- Every candidate in the cluster, and any candidate outside it that sees both colors of its digit.
- Result
- Either every candidate of one color goes, or single candidates that see both colors go.
- Tell-tale
- A grid full of cells with two candidates, where simple coloring on any one digit stops after a link or two.
- If it fails
- If no rule fires, grow the cluster further or start from another cell with two candidates.