We're now moving into techniques that require you to eliminate candidates before you can find more hidden or naked singles. Pointing is a situation where a particular number can only possibly go in one row (or one column) within a box. This means logically that it can't appear in that row (or column) in either of the other two boxes, so any occurrence of that number as a candidate can be eliminated from the other boxes which share the same row/column. It "points" down the row or column and eliminates anything it can see in other boxes sharing the same house
The term "direct" is a special case where the eliminations directly reveal a hidden single that you can immediately fill in. This is a slightly simpler form of pointing which can be done without having to write down and track candidates (you can do it in your head and fill in a number!), but we shall look at pointing in general a bit later on where there are only eliminations and no hidden singles are revealed. This is where you'll need to keep track of any eliminations you've made.
In this example, looking at Box 4, the number 2 can only go in row 5 (it's prevented from going in B4 or B5 / r45c2 by the '2' in B1 / r1c2). This means that the '2' cannot appear in Row 5 in either Box 5 or Box 6 and can be eliminated as a candidate from those two boxes as '2' must go in either A5 or C5.
This can be notated in row/column/box form as: 2 in b4 => r5c4568<>2. This means that the 2 in box 4 (2 in b4) leads to (=>) row 5, columns 4,5,6 & 8 not equalling 2 (r5c4568<>2).
Now you know that r5c8<>2 (H5 can't be 2), then that leaves r6c8 (H6) as the only possibility for number 2 in box 6 - a hidden single (notated as r6c8=2). The revealing of this hidden single is what makes this "direct" pointing.
The terms and notation might seem a bit confusing at first, but don't worry - you'll get used to it! See Understanding the Grid for a quick overview.
This time the cells in box 2 (r23c5 or E2,E3) are "pointing" down a column - one of these two cells in the same column and box must be the number 1, we don't know which yet, but it can't possibly go in box 5 or 8 in column 5 and can be eliminated. This can be written as 1 in b2 => r789c5<>1, leaving r7c4=1, or D7 as a directly revealed hidden single for box 8.
So to recap, look within a box for a candidate number that appears only in one row or one column. You can then eliminate that number if they appear in the same row/column in either of the two other boxes.
There is another direct pointing hidden within this grid. See if you can spot it, and the hidden single it reveals. Hint: it involves the candidate number 5.
There are also 3 other pointings in the grid, which allow you to eliminate candidates, but they don't give you a concrete hidden single to fill in, so although essentially the same concept they aren't "direct".
Naked Singles | Direct Claiming
Play online sudoku now or check out our 300 Sudoku Puzzles: Easy to Extreme book! Or start off with 150 Easy Sudoku Puzzles.
