Strategies for Popular Number Puzzles


  • Almost Locked Set (ALS) – A set of N unsolved cells with N+1 candidates
  • Bi-location – A unit with only two occurances of a candidate X
  • Bi-value – A cell with only two candidates remaining
  • Box – Any 3x3 shaped unit in a normal sudoku, or any squiggly 9-cell shape in Jigsaw sudoku which must contain 1 to 9. There are 9 boxes in 9x9 sudoku.
  • Cage – A marked off group of cells for which their sum is provided in Killer Sudoku and variants.
  • Candidate – A possible solution for a cell. Any cell reduced to one candidate is solved.
  • Cell – A square on the sudoku grid for which there is one single number solution.
  • Chain – A sequence of links between candidates such that the two ends imply an elimination. All Loops are closed chains.
  • Conjugate Pair – The two remaining candidates in a bi-location are conjugate. They are used to form strong link within a unit since one must be true and the other must be false.
  • Contradiction – In Sudoku an illegal and therefore contradictory situation can occur if a) there are no candidates left in a cell, or b) two or more cells claim to be true. The aim of many strategies is to show a contradiction.
  • Continuous – In a Loop it signifies that the links between nodes strictly alternate between strong and weak links.
  • Cycle – Another name for a Loop. See Loop.
  • Discontinuous – In a Loop it signifies that there is one discontinuity where a node is beset by either two weak links or two strong links.
  • Grouped Node – A set of candidates of the same value (that must share a unit) that can be used to form a group with the effect of being able to treat it as a single cell.
  • Hinge – In a Y-Wing the middle cell which joins the two pincer cells.
  • Inference – Valid deductions that can be made between two linked candidates. There are inferences of the weak kind and the strong kind.
  • Locked Set – A group of N candidates confined to a group of N cells. All candidates that can see a locked set can be removed. Naked Pairs, Triples etc are Locked Sets.
  • Loop – Another name for a Cycle. See Cycle. A closed chain or sequence of candidates (which are called nodes in the loop) used to make a deduction. Loops are continuous or discontinuous.
  • Pincer – In a Y-Wing or Y-Wing Chain the two end nodes are pincers which attack a cell for the purposes of elimination. See also Hinge.
  • Strong Inference – Where two candidates X and Y are linked with strong inference then both cannot be false at the same time. Therefore if X is false Y is true and if Y is false X is true.
  • Strong Link – A link between two candidates (which can be a single number or a grouped node) whereby if one is deemed false the other must be true. Strong Links can be between two cells (bi-location), within a call (bi-value) or as part of an ALS or more complex structure. Article here
  • Unit – My preferred term for any row, column or box. Also called a house.
  • Variant – A variation on an original puzzle, eg Jigsaw Sudoku is a variant of Sudoku.
  • Weak Inference – Where two candidates X and Y are linked weak inference implies that both cannot be true at the same time. Therefore if X is true Y is false and if Y is true X is false.
  • Weak Link – A link between one candidate and all others in a unit or cell whereby if the candidate is deemed to be true all the others are false. A strong link can be deemed to be weak merely because "all the others" includes cases where there is only one other. Article here
  • XY-Wing – Another name for Y-Wing
The following terms are not used on this site but may be found out in the wild
  • Block – Another name for a box
  • Chute – Three boxes in a column.
  • Domain – Another term for a unit.
  • Given – Another name for a clue.
  • House – Another name for a unit, sometimes also the same as a chute.
  • Reduction – Another name for elimination
  • Region – Another name for a box



... by: Marty

Saturday 2-Dec-2023
Whatever happened to Sadman? Used him for years! Found an old version, put it up on new PC, timed out after 30 days and now unusable. I'm a Yale math grad, but not a great mathematician, and too old (95) to learn new tricks, since they evaporate too soon! Any advice? -Marty

... by: DaveK

Friday 9-Jun-2023
Is there any convention to the bracketing used here? eg. { } or [ ] or ( )

Sometimes i see eg. of (2/2/3) or {2/2/3} does it mean the possibility of 2, 2, 3 in the next 3 cells, row or columnwise?

thanks & regards,
Andrew Stuart writes:
I started using [ and ] for grouped cells since that extended single cells +8[A2] etc and this was before Almost Locked Sets in chain links. Then I picked { } for ALSs in chains as it helped to distinguish them. Not enough brackets for every type. As for sets of candidates there may be some inconsistency between () and {}. - [Del]
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