Technique Guide

Rules

• Circle exactly one of each number from 1 to 9.
• Each row, column, and block must contain exactly one circled number.

Definitions

cell: one of the 81 little squares that make up the board

row: horizontal group of 9 cells. Row 1 is on the top.

column: vertical group of 9 cells. Column 1 is on the left.

block: 3x3 group of 9 cells, outlined by bold lines. Block 1 is in the top-left.

group: a row, column or block

R#C#: cell coordinates. (Eg. R3C6 means the cell in Row 3, Column 6.)

candidate: a number that has not been crossed out or circled yet

see: two candidates "see" each other if they are in the same row, column or block, or if they are the same number. (They cannot both be circled.)

technique: a pattern of logical reasoning used to get closer to the solution. Spot a particular pattern, then cross off or circle something!

Technique: Single Candidate For Group

If: a row, column or block has only one candidate remaining

then: circle this candidate.

Eg. Row 5 has only one candidate: #5.

Whenever you circle a number, cross out all other candidates in the same row, column and block as the circled number.

Also cross out all other candidates with the same number as the circled number. (In this case, all other #5s.)

Technique: Single Candidate For Number

If: there is only one candidate for a number remaining on the board

then: circle this candidate.

Eg. There is only one #7 candidate remaining on the board.

Technique: Single Group For Number

If: all candidates of a particular number are in the same row, column, or block

then: cross off all candidates in this group that are other numbers.

Eg. All #1 candidates are in Block 4.

Technique: Single Number In Group

If: all candidates in a row, column or block are the same number

then: cross off all candidates of this number that are outside of this group.

Eg. All candidates in Row 1 are #9s.

Technique: All Candidates In Block Are In The Same Row Or Column

If: all candidates in a block are in a line (same row or column)

then: cross off all candidates outside this block in the same row or column.

Eg. All candidates in Block 1 are aligned (in Column 1).

Technique: All Candidates In Row or Column Are In The Same Block

If: all candidates in a row or column are in the same block

then: cross off all candidates in this block that are outside of this row or column.

Eg. All candidates in Column 7 are in Block 6.

Technique: Candidate Sees All Candidates Of Number

If: a candidate sees every candidate of a number

then: cross out this candidate.

Eg. Candidates at R4C6 and R8C2 can see all #3 candidates.

Eg. Candidates at R4C5, R5C8, and R5C9 can see all #8 candidates.

Tip: temporarily circle all candidates of a particular number so you can see them easily. Uncircle them again when finished looking at them.

Technique: Candidate Sees All Candidates Of Group From Outside

If: a candidate sees all candidates of a row, column or block, and is outside of this group

then: cross off this candidate.

Eg. The candidates in R1C7, R3C8, and R6C3 can see all candidates in Block 6 from outside.

Eg. The candidate in R2C6 can see all candidates in Row 1 from outside.

Technique: Matching Pairs

If: two groups both contain only candidates of the same two numbers

and: the groups do not share any candidates

then: cross off all candidates of these two numbers that are outside of these two groups.

Eg. #5 and #9 are the only two numbers in Block 4 and Block 6.

Eg. #2 and #5 are the only two numbers in Row 2 and Block 5.

Technique: Matching Triples

If: three groups each contain only candidates of the same three numbers (or fewer)

and: the groups do not share any candidates

then: cross off all candidates of these three numbers that are outside of these three groups.

Eg. #1, #4, #6 are the only three numbers in Block 4, Column 5 and Row 8.