BrainPuzzles

Pointing pair

A digit that can only sit in one row or column inside a box. It has not been placed yet, but it has already claimed that line.

How to spot one

  1. Pick a box and a digit, and mark every cell in the box where that digit can still go.
  2. If they all sit in one row (or one column), the digit is somewhere in that row inside this box.
  3. So it cannot be anywhere else in that row. Cross it out of the rest of the row, outside the box.

A real example

This grid is not a drawing. It came out of our generator, and the position below is one a solver actually reaches: every digit the reasoning uses is on the board, so you can check it yourself without taking anything on trust. The reasoning sits in column 2, shaded blue. The cells it looks at are green; the cells it changes are amber.

891663817127486891719291847845636767
In box 1, 4 can only sit in column 2, so 4 is gone from the rest of that column. So r5c2 loses that candidate.

The same move on a different grid

One example can be a fluke of the grid it sits in, so here is another, dug at hard from the seed second:pointing:100 with 28 starting digits. The technique fires in a different place, for a different digit, and the point is what it buys you afterwards.

4937911478597514351784926641975683255476951962
In box 1, 3 can only sit in row 3, so 3 is gone from the rest of that row. So r3c8 loses that candidate.

What the solver does next, from exactly that position:

  1. hidden single — In column 2, 6 has only one cell left it can go in. r1c2 takes 6, the only digit it had left.
  2. naked pair — Two cells in box 1 can only be 2 or 3, so between them they use both and no other cell in box 1 can be 2 or 3. r1c1, r2c1 give up that candidate.
  3. naked pair — Two cells in column 1 can only be 5 or 8, so between them they use both and no other cell in column 1 can be 5 or 8. r4c1, r9c1 give up that candidate.

That is the pay-off a pointing pair is worth: not the one cell it names, but the run of cheap moves it unlocks behind it.

Where you meet it

Our grids are graded by the hardest technique they force, so a pointing pair is what makes a hard grid what it is. Needs a pair or a locked digit. When you ask for a hint on one of them, the first thing the game says is the name of the technique and which row, column or box to use it in, and that step costs nothing — you still get to find the cell yourself.

The other techniques

Ready to use it? Play hard sudoku, take on the daily grid, or start from how to play.