Single number techniques

This group of techniques considers just single number values. This means all pencil marks of other numbers can be ignored.

Lone single

Lone singles are cells where just one number can be inserted. Sometimes they might be not easy to spot. When pencil marks are added then spotting them gets easy.

The following is a cell containing lone singles for 3,6,8,9

Hidden Single

If a number is just possible in one block, row or column then the number can be set and therefore all other pencil mark in this cells can be erased.

The example below has the hidden single 7. The additional pencil marks 5 and 8 make it more difficult to spot.

Intersection with block

Even when it is not clear where to set a number, some pencil marks can be removed:

Rows and columns intersect with blocks. This intersection contains 3 cells in a line.

If this intersection has the same amount of number as the row or column, then the block can not have the numbers in other cells.

The top row has two 3. Both are in the first block (intersect). So one of the two 3 must be a there and all other pencil marks with 3 in the other rows of the first block can be removed.

X wing

When looking to the two columns, the following can be observed:

The number 8 occurs in the two columns 2 times and on exactly the same rows. The four 8 form an cross or X. It is still not clear where the two 8 are but it can be said that the two 8 must be in the 4 intersections of the two columns with the two rows. All other 8 pencil marks on the rows not intersection with the two columns can be removed.

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