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Strategies for Popular Number Puzzles

Getting Started

Every puzzle from the easiest to the hardest requires simple 'eyeballing' to detect the easy solutions. You certainly need to start the puzzle by checking for simple placements and when you have cracked a puzzle the last ten or twenty cells will fall into place just by letting your eye scan the board. You are looking for any unsolved cell that is the last possible place a number can go in a row, column or box. There are a number of patterns to look out for.

The convention on this site is to refer to columns with numbers, rows with letters (I is skipped since it looks like 1 and we use J). Box numbers may not be so obvious, so to the right is a plan of them). There is also a Glossary of terms.

Last Remaining Cell in a Box

Last number in a Box
Last number in a Box : Load Example
This easy puzzle will demonstrate 'eyeballing'. It is best to start with boxes as they are the easiest shape to work with. Box 7 seems rather crowded with four clues so it's a good bet that some of these cells can be filled in quickly. Looking at the 8s on the board I can see that the 8 in D3 occupies the whole column and prohibits any 8 in H3 and J3. Likewise the 8 in G5 fills in the whole row preventing any 8 from being placed in G1 and G2.

So the last remaining cell in box 7 for an 8 is H1.

Last Remaining Cell in a Row (or Column)

Last number in a row
Last number in a row
When you have scanned the boxes for obvious solutions, check the rows and columns. The arrangement of 4s on this board suggests something in the first row, row A. We have a 4 in G3 which occupies the space in A3. Likewise the 4 in F7 removes A7 as a placement for 4. And the 4 in box 2 uses up all the places in A4 and A6.

So the last remaining cell for 4 in the row is A2.


Last number in a row, column and box
Last number in a row, column and box

Sometimes there are several reasons for a placement. This 4 in J8 is a great example. In blue I have shown that 4 in J8 is the last remaining number in terms of the box it is in. The red + blue lines show it is the last number in column 8 and the green + blue lines demonstrate it is the last number in row J.

This 4 has been pinned to the board quite conclusively.

The Last Possible Number

The Last Possible Number
The Last Possible Number

Eyeballing is actually quicker than checking each cell for the last possible number, but it is a valid approach, so I include it here. It is the sort of strategy a beginner thinks of when faced with the puzzle for the first time. It is best used when a cell stands out because all the other numbers seem to be in place.

Here the 5 in B1 can be determined because every other number from 1 to 9 apart from 5 is present in either the row, column or box (marked in green).
In the jargon, this is a Naked Single - if you were using candidates at this stage it would be the only candidate in the cell. The 'eyeballing' techniques help determine Hidden Singles since other candidates are possible in those places but at least one candidate is unique to a particular row, column and box. You can see this difference if you 'Take Step' with candidates turned on.

Continue to Naked Candidates


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Comments Talk

Tuesday 7-May-2019

... by: peter

In the "Last possible number", why can't the 5 be in B-2, B-3, B-5 or B-7?
Andrew Stuart writes:

On the face of it 5 certainly ‘fits’ in any of the free cells in row B, given the information we have on 5. But the question looking at B1 is not “where can we fit 5 in row B?” but what numbers are available in B1?” That leads us to the answer that ONLY 5 can fit there, so the other free spaces are moot.

Thursday 28-Mar-2019

... by: Romeo

It's easy to understand and helpful in finding solutions

Saturday 4-Aug-2018

... by: STS

Till I read the above artucke, I used to 'name' each square on Sudoku board by naming the columns from left to right as A to H and Z and the rows bottom up as 1 to 9.

This is how squares in a chessboard are named.

Saturday 4-Aug-2018

... by: STS

Till I read the above artucke, I used to 'name' each square on Sudoku board by naming the columns from left to right as A to H and Z and the rows bottom up as 1 to 9.

This is how squares in a chessboard are named.
Andrew Stuart writes:

Following the conventions used since discussion began in 2005. Wish I could say I was so early I chose that, but no!

Thursday 24-Nov-2016

... by: Paul

pcw - persevere! I'm nearly 80 and no brain box. But I enjoy tackling Sudoku and slowly improving my solving skills.

Saturday 20-Aug-2016

... by: wrsides

good lessons

Friday 1-Jul-2016

... by: Thyge

I use dots to represent the numbers possible in a cell. A dot in the top left corner is 1, the top middle is 2, and top right is 3. Likewise, the middle part has dots for 4, 5, and 6, and the bottom the numbers 7 through 9. This gives me a dot pattern to help eliminate numbers in a row, line, or box. A dot kan easily be x'ed out when the corresponding number has been eliminated. :)
Andrew Stuart writes:

A good method I've seen used quite a lot

Wednesday 28-Oct-2015

... by: pcw

I guess I'm just losing it as I age--this is much too complicated for me. But thank you nonetheless for creating and sharing. Brighter minds than mine will enjoy.

Saturday 20-Jun-2015

... by: jb681131

You should also add the more evident solving method call "Full House" where the digit to find is the last digit in its house (row, col or box). Also called "Last Digit" if it's the last digit on the board.

Sunday 3-May-2015

... by: George

I'm wanting to get better at solving the puzzles.

Saturday 10-May-2014

... by: james reinoso

buenos dias
el ejemplo que muestran por que en B1 va el 5 por favor expliquenmelo

Thursday 6-Mar-2014

... by: chebob

just hooked, trying to get the jist of puzzle/

Tuesday 19-Nov-2013

... by: Satish Gupta

After 17 months, I believe there is no website even half as good as this. Congratulations to all at Sudokuwiki Organisation

Friday 23-Aug-2013

... by: Danis

Simple really.
1 LOOK BEFORE YOU LEAP. check to see if there is any other number that can fit in a box before you write one in.
2 PENCIL IN POSSIBILITIES. write very faintly what numbers can fit in a box. (eg if there is 3 possible numbers then write them in the real small, and then when you put one of those numbers in that row/column/large box, simply cross it out) eventually you'll have 1 nubemr penciled in, and that MUST be the number that goes there.
Hope that helps. (step 2 seems to be the most affective)

Monday 19-Aug-2013

... by: edmark


Sunday 28-Jul-2013

... by: Huskidawgs-

I'm a fresh newbie so maybe I don't get it, but in the "last number in a row" example, why could not a 4 be placed in B1? The 4 in Box B should only remove Row C and Column 5, shouldn't it?
Andrew Stuart writes:

Looking at 4s from the point of view of the box gives us three places 4 could be, including B1 - none contradicts the rules. A2 or B2 will also do. So we can't decide based on the box. The way to choose which is right - in this case - is determined by the fact that in the row there is only once place for a 4. There will be *some* easy puzzles that can be solved only by looking at how to fill boxes, but it's easy to check rows and columns as well for a faster completion.

Wednesday 13-Feb-2013

... by: Mike

I enjoy doing the puzzles in the newspaper
I got bord with the Jumble so I moved on to the
celebrity cipher and mastered that one .My brother got me started with Sudoku and its really a
challenge .Just started it last week. I think the eyeballing is a good way to start. great web
site, keep up the good work.


Sunday 13-Jan-2013

... by: Anon

After years of struggle, I decided to go to basics - and used my "eyeball". Thank you for this piece.

Tuesday 8-Jan-2013

... by: Amir Latif

I developed something I call an "Index." You make a list of all the numbers NOT appearing in a column, or row, or even a square. Test the index against each blank position in the column. If you get a match in the neighbourhood for each number in the index but one, that number goes in the blank cell. The "neighbourhood" includes the contents of the row, column and square that that blank cell is in,
It may not always work, and often you may have to do some manual testing.

Please tell me that other people are using this device which came to me.
Blessings, Amir

Monday 7-Jan-2013

... by: cliff

Getting started really made the puzzle simplier I love this puzzle its a great
brain teaser

Tuesday 20-Nov-2012

... by: ly ousmane

it's my 1st time and i have no clue whatsoever of solving it,don't even know where to start.

Friday 27-Apr-2012

... by: Satish Gupta

It is the best thing I have seen about sudoku which I got exposed to about 10 days ago
Article created on 25-January-2012. Views: 642951
This page was last modified on 14-April-2012.
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