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Hidden Singles

Hidden singles are a simple enough concept, but are often quite hard to spot.

The definition of a hidden single is when a pencil mark is the only one of its kind in an entire row, column, or block.

For example, can you find one in the sample below?

This row must have a "7" in it somewhere, because in Sudoku all rows have a "7". If you look closely at the pencil marks, you will see only one cell that has a "7" as one of its candidates.

What does this mean? Simple. That cell must be the "7"! Erase all the other pencil marks, fill in the "7" with your pen, and erase any other "7" pencil marks in the same column or block (we already know there aren't any in that row!).

Similarly, the below sample shows there is only one "4" pencil mark in the entire block:

As I said, the problem with these guys is that they're hard to find! In order to perform an exhaustive search, you need to look at every row, column, and block, for each of the numbers, 1 through 9. This means nine rows, nine columns, and nine blocks (these are sometimes referred to as the 27 different "houses"), for nine different numbers. That's 243 (27 x 9) different searches!

OK, I may have overstated it a bit for effect. The truth is, you wouldn't scan a row for a single "5" pencil mark if the row already had a "5" in it. Also, many times a "house" (row, column, or block) will only have two or three cells left to fill in, and then they are much easier to spot…

Computer programs can make this easier, as well. Sudoklue, for example, will highlight all the pencil marks of a given number if you press CTRL + [number]. See the screenshot below after I've pressed CTRL + 5:

This makes the hidden single "5" in the center much easier to spot.

Of course, some may consider getting help like this "cheating"…

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