Variant Sudoku

Chains

A chain is a list of “if this cell isn’t the digit, then that cell is” steps. When the chain starts and ends on the same digit, one of its two ends must be that digit.

Practice now
7
5
3
9
3
2
6
7
4
8
1
8
9
3
7
569
16
4
8
39
5
7
69
13
2
2
9
1
4
8
6
8
7
1
2
4
1
3
2
6
9
7
5
8
5
2
9
7
3
8
1
4
6
Clear 6 from cells that see both ends.

Why it works

On the board above:

Every cell in this chain has only two candidates.

If r4c8 isn’t 6, then r4c8 is 1, so r5c8 isn’t 1, so r5c8 is 3, so r5c4 isn’t 3, so r5c4 is 9, so r5c7 isn’t 9, so r5c7 is 6.

So either r4c8 is 6 or r5c7 is 6.

r4c7 sees both ends, so it can’t be 6.

How to spot it

  1. X-Chain: one digit

    Hop between spots of one digit through houses where it has only two spots.

  2. XY-Chain: two-candidate cells

    Hop from cell to cell. Each cell has two marks, and each hop passes the shared digit along.

  3. End on the same digit you started

    The chain must start and end on the same digit, in different cells.

  4. Clear cells that see both ends

    Only those cells lose the digit.

Practice

Real boards from the solver, with every pencil mark filled in. Spot it, then use it, then find it cold.

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Try it in a real puzzle

Each of these needs a chain to finish. It opens in the player.

Tips

Keep chains short

Short chains are easier to check. Four to six links is plenty.

Coloring is a chain

Simple Coloring is a chain that branches. If you can color, you can chain.

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In the glossary

X-chainXY-chain