Solver App for Android and iPhone
Strategies for Number Puzzles of all kinds
Page Index
Solvers
Puzzles
Basic Strategies
Tough Strategies
Diabolical Strategies
Extreme Strategies
Depreciated Strategies
Str8ts
Other

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 in a row, column or box for a number to go. There are a number of patterns to look out for.

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 quickly. Looking at the 8s on 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

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 suggest 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, A5 and A6.

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

Pinned!

Last number in row, columns and box
Last number in row, columns and box


Sometimes there are several reasons for a placement. This four 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 lines (plus blue lines) show it is the last number in column 8 and the green 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


Comments

Your Name/Handle

Email Address - required for confirmation (it will not be displayed here)

Your comment or question

Please enter the
letters you see:
arrow
Enter these letters Remember me


Please keep your comments relevant to this article.
Email addresses are never displayed, but they are required to confirm your comments. When you enter your name and email address, you'll be sent a link to confirm your comment. Line breaks and paragraphs are automatically converted — no need to use <p> or <br> tags.
Talk Subject Comments
Comments here pertain to corrections to the text, not the subject itself

Monday 29-Apr-2013

... by: Thos

In the section "Pinned" you state 3 times that J8 is the last "number in ..." Actually J8 is the last "cell in ..." isn't it?
Andrew Stuart writes:

Edited that sentence, your point is correct

Article created on 25-January-2012. Views: 146288
This page was last modified on 14-April-2012.
All text is copyright and for personal use only but may be reproduced with the permission of the author.
Copyright Andrew Stuart @ Syndicated Puzzles Inc, 2012