Double-cat strategy · step 3 of 4

The stretch squeeze

Cats can’t sit side by side, so every stretch of open squares has a hard capacity — and a line that owes two cats can be read like a sum. Count the stretches and the board starts moving by arithmetic.

The rule in one line: a stretch of L consecutive open squares holds at most ⌈L/2⌉ cats, because every cat needs a gap after it. So: 1 square fits 1 cat, 2 squares fit 1, 3 squares fit 2 (only as the two ends), 4 fit 2, 5 fit 3. Crossed-out squares break a line into stretches; add up the capacities and compare the total against how many cats the line still needs.

When the count is exact, cats are forced

The middle row still needs both cats, and its only open squares are one stretch of three. Three squares fit two cats exactly one way: the two ends. Both are placed on the spot.

A stretch of three holding two cats has no freedom at all — center-plus-anything touches. So when crosses reduce a two-cat line to a single three-stretch, you don’t learn something, you learn everything: both ends are cats, right now. The same logic in looser forms: a two-cat line whose stretches are a singleton plus anything must use the singleton; a stretch of five holding three cats fills squares 1–3–5.

The squeeze from the next row over

The bottom row needs both cats and has a two-stretch (fits one) plus a three-stretch (fits two). A cat on the highlighted square would blot out the entire three-stretch below it — leaving room for just one cat. Cross it.

Here is where the stretch count earns its keep: a cat pressing down from a neighboring row wipes out up to three squares of the stretch beneath it. Before placing anything next to a tight line, redo the count as if the cat were there. If the line can no longer fit its remaining cats, the square is a guaranteed cross — no what-if chain required, just capacity arithmetic.

This exact position — a two-stretch plus a three-stretch, and a candidate square hovering over the middle of the three — is lifted from a real Duckdoku double-duck level; it was the deduction the whole board hinged on. Columns work identically: a cat beside a tight column eats up to three of its squares.

The five-second habit

• Whenever a line drops to two stretches, say the count out loud: “one plus two — needs two — tight.” A tight line forbids every neighboring square that would break its count.
• An exactly tight line (capacity = need) also forces its singletons: a one-square stretch in a tight line is a cat.
• The pair squeeze is this same idea with the counting hidden; when the survivors don’t sit in one line, use that instead.

MeowSolver shows both faces of this technique as a Stretch squeeze hint — forced cats when a line’s count pins them, crosses when a placement would sink a nearby line — with the line’s stretches outlined so you can re-count them yourself.

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