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Grid technique · Intermediate

Set Transposition

The locked-pair idea applied across categories: if a locked pair in one mini-grid lines up with a locked pair in another, the two pairs' possible subjects are the same set.

Why it works

If two items are confined to exactly the subjects holding a locked pair, their subject sets are identical to that pair's, so an elimination against one pair transfers straight across to the other.

Trigger

A locked pair in one mini-grid, plus a second pair of items in another category confined to the exact same two subjects.

Common mistake

Treating the two mini-grids as unrelated once the first locked pair is found, instead of checking whether a second category is locked to the same two subjects.

Example

If price is locked to Mina/Theo, and colour is separately locked to Mina/Theo, an elimination against one price-holder eliminates the matching colour too.

On Bambleweeny's board

Confirmed in the live solver as the k=2 case of this technique. A generalised k>2 version was investigated and found to add nothing new — Two-Bridge Elimination already reaches the same conclusions first.

Put it to work

See this technique on a live board, or go back and browse the rest of the library.