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Learn

One technique per lesson, shown on a real grid.

Easy

  1. Full houseWhen a row, a column or a box has a single empty cell left, that cell takes the one digit still missing there.
  2. Hidden singleSometimes a digit fits in only one cell of a row, a column or a box: every other empty cell there already sees that digit, in its own row, column or box.

Medium

  1. Naked singleSometimes a cell can hold only one digit: the eight others are already in its row, its column or its box.
  2. PointingWhen, inside a box, every place left for a digit lies in the same row (or column), the digit of that box is on that line.
  3. ClaimingWhen, along a row (or column), every place left for a digit lies inside the same box, the digit of that line is in that box.

Hard

  1. Naked pairTwo cells of the same row, column or box that can only hold the same two digits share them: one cell gets each.
  2. Hidden pairWhen two digits can each go in only the same two cells of a row, a column or a box, those two cells hold those two digits.
  3. Naked tripleThree cells of the same row, column or box that, between them, can only hold the same three digits take those three digits.
  4. Hidden tripleWhen three digits can only go in the same three cells of a row, a column or a box, those cells hold those three digits.

Expert

  1. X-wingTake one digit.
  2. SkyscraperTake one digit and two rows where it has exactly two places each.
  3. 2-string kiteTake one digit, a row where it has exactly two places and a column where it has exactly two places.
  4. XY-wingAn XY-wing is three cells with two candidates each.
  5. XYZ-wingAn XYZ-wing is an XY-wing whose pivot has a third candidate: the pivot holds XYZ, and it sees two pincers holding XZ and YZ.
  6. W-wingA W-wing starts with two cells holding the same pair, XY, that don’t see each other.
  7. SwordfishA swordfish is an X-wing with three rows.
  8. Naked quadFour cells of the same row, column or box that, between them, can only hold the same four digits take those four digits.
  9. Hidden quadWhen four digits can only go in the same four cells of a row, a column or a box, those cells hold those four digits.
  10. JellyfishA jellyfish is the next fish after the swordfish: four rows where one digit’s places all fall in the same four columns.

Master

  1. Simple coloringSimple coloring follows one digit.
  2. X-chainAn X-chain follows one digit from cell to cell.
  3. XY-chainAn XY-chain links cells that have exactly two candidates, each seeing the next and sharing one digit with it.
  4. Alternating chainAn alternating chain mixes the X-chain and the XY-chain.