Edges and corners

This page covers rules on a pair of adjacent cells (6.6) and on a 2×2 block (6.7).

6.6 edge

Exactly 2 orthogonally adjacent cells.

kind	Fields	Meaning	Drawing
kropki	color: "white" | "black"	White: |a − b| = 1. Black: one digit is double the other. A 1–2 pair may carry either colour.
xv	letter: "X" | "V"	X: a + b = 10. V: a + b = 5.
difference	value k	|a − b| = k.
sum	sum s	a + b = s.
product	value p	a · b = p.
ratio	value k	one digit is k times the other.
greater	–	cells[0] > cells[1]; the order matters.

A numbered clue (difference, sum, product, ratio) must be made by some pair of different digits 1..D (the two cells always share a row or column, so their digits differ); a value no pair makes is refused.

kropki white and difference 1 mean the same to a solver but draw differently; both exist on purpose (likewise black / ratio 2 and X, V / sum 10, 5). Canonical writers that cannot tell them apart write kropki and xv.

6.7 corner

Exactly 4 cells forming a 2×2 block, written TL, TR, BL, BR.

kind	Fields	Meaning	Drawing
battenburg	–	The 4 cells form a parity checkerboard: TL and BR share a parity, TR and BL the other.
mathrax	op: "+", "-", "x", "/" with value; or op: "even" / "odd"	+ - x /: each diagonal pair (TL–BR and TR–BL) combines to value (difference and quotient are larger over smaller). even / odd: all four digits have that parity.
exclude	value	None of the 4 cells holds value.

Digits that must appear around a corner (a quadruple) are a contains rule on the 4 cells (6.13); it is drawn as a corner circle.