Single Digit Sudoku Techniques: Skyscraper to Turbot Fish

What single digit Sudoku techniques share

Single digit Sudoku techniques all study one candidate at a time and use its geometry to force an elimination, without caring about any other number on the board. They live between basic fish and full chains in difficulty, and they are wonderful to learn because you can hunt them by scanning just one shape. In Shapedoku that is literal: pick the orange triangle and ignore everything else. Each pattern below relies on conjugate pairs, houses where the chosen digit has exactly two possible cells. When two conjugate pairs share a line or a box, a squeeze appears. The four patterns here together resolve a huge number of tough positions, which is why single digit Sudoku techniques are such an efficient thing to study early.

The skyscraper

A skyscraper uses two conjugate pairs pointing the same way. Say 6 appears only twice in column c2, at r1c2 and r8c2, and only twice in column c7, at r1c7 and r5c7. The two pairs share row r1, which forms the base. The far ends, r8c2 and r5c7, are the tops of the two towers. One of those tops must be a 6, so any cell seeing both, such as r8c7 or r5c2, cannot be 6 and you erase it. The trick to spotting a skyscraper is finding two conjugate pairs that line up at one end and splay apart at the other. Once you train your eye for that shape, skyscrapers appear on nearly every Hard grid.

Two-string kite and empty rectangle

A two-string kite is the skyscraper rotated so the two conjugate pairs run in different directions, one along a row and one along a column, joined by sharing a single box. If 4 has a row pair in r3 and a column pair in c8, and both pairs pass through box 3, then the two loose ends see each other through the kite, and a cell seeing both ends loses 4. The empty rectangle is subtler. It looks for a box where a digit is confined to a single row and single column crossing inside it, forming an L, then pairs that box with a conjugate pair elsewhere on the matching line to eliminate at the intersection. Empty rectangles are prized because they need only one conjugate pair plus a box pattern, so they turn up when cleaner fish do not.

Turbot fish and how they connect

Turbot fish is really an umbrella name. Any of these single-digit patterns can be described as a turbot fish, a short chain on one digit with two strong links and a weak link between them. Recognising that is freeing: once you can see a skyscraper, you have already learned the turbot fish, and the two-string kite is just its bent sibling. Rather than memorising four separate diagrams, hold the single idea of two conjugate pairs connected by a shared house, then read whichever shape the grid hands you. Practise by choosing one digit and sweeping the whole board for conjugate pairs before looking at anything else. Shapedoku helps because a single glowing shape is easy to isolate, its Notes view with smart cleanup keeps the candidate map trustworthy, and the first free hint can explain why a shape fits; the free solver at shapedoku.com will surface a skyscraper or kite when a grid has you stuck.

• Skyscraper: two same-direction conjugate pairs sharing a base line.
• Two-string kite: a row pair and a column pair sharing one box.
• Empty rectangle: a digit confined to an L in a box, paired with a conjugate pair on the line.
• Turbot fish: the umbrella name for these two strong links plus a weak link.