3D Medusa (Advanced Coloring)

Prerequisite: Basic Coloring

Overview

3D Medusa is an “upgraded coloring” technique: it still uses two colors (blue / yellow) to represent two mutually exclusive deduction routes, but it no longer focuses on just one digit — it can connect multiple digits into one reasoning network.

What makes it stronger is that it uses more than one kind of strong link:

• Conjugate pair (strong link): in a row/column/box, a digit has exactly 2 candidate positions
• Bivalue cell (strong link): a cell has exactly 2 candidates

After coloring along strong links, you can think of blue/yellow as two opposite assumptions:

• Assume blue is true ⇒ yellow is false
• Assume blue is false ⇒ yellow is true

So within the same colored component, one of the two colors must be true.

3D Medusa most commonly gives two kinds of conclusions:

1. Trap: a red candidate conflicts with both the blue route and the yellow route → eliminate the red candidate
2. Same-color contradiction: two same-color candidates conflict in a house (or a cell) → that entire color is impossible and can be eliminated

If you’re not comfortable with strong/weak links yet, read: Chain Basics.

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Trap

In the image above, we color candidates along strong links. The chain includes candidate 9 in r3c5 (blue), and it also reaches candidate 6 in r4c5 (yellow).

In the image above, the red candidate to eliminate is candidate 9 in r4c5.
Why can we remove it? The key idea is “one of the two colors must be true”:

• If blue is true, then the blue candidate 9 in r3c5 is true, so the red candidate 9 in r4c5 conflicts with it and cannot be true.
• If blue is false, then the yellow route must be true; since candidate 6 in r4c5 (yellow) is true, r4c5 cannot also be 9 (same cell), so the red candidate 9 in r4c5 still cannot be true.

Either way, the red candidate is impossible, so it can be eliminated.

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Same-color contradiction

In the image above, candidate 2 in r8c2 and candidate 2 in r8c7 are both colored yellow.
But they are in the same row, so they can’t both be 2 — that’s a same-color contradiction.

Therefore the yellow route is impossible, and all yellow candidates in that colored component can be eliminated (they are marked red in the image).

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How to Find 3D Medusa

One-line checklist: build a strong-link network (conjugate pairs + bivalue cells), color it blue/yellow, then look for traps or same-color contradictions.

In a real puzzle:

1. Find strong links from conjugate pairs and bivalue cells
2. Color candidates along strong links (blue/yellow are mutually exclusive)
3. Look for:
   • a red candidate that conflicts with both color routes → trap elimination
   • two same-color candidates that conflict in a row/column/box (or a cell) → eliminate that entire color