Simple Colouring

The example here is from a puzzle which I published in February 2021. I solved it as far as I could before arriving at the position below:

I used simple colouring to move forwards as you can see in the next picture:

If row 1 column 2 is 5:
Row 1 column 7 cannot be 5.
Row 3 column 9 must be 5.
Row 5 column 9 cannot be 5.
Row 5 column 2 must be 5.
However, there is already a 5 in row 1 column 2 so this is not possible.

I will leave you to follow all the scenarios resulting from the assumption that row 1 column 2 is 5. None of them work so all the candidates marked in yellow can be removed.

The other possibility is that row 3 column 3 is 5.
This is marked in blue and does not lead to any contradictions so it is the correct answer.

Hidden Single in a Box

I published the puzzle below in 2014:

 

Look at the 3x3 box or mini-grid number 6 i.e. the one with the clues 3, 4 and 8.

Where does the number 1 go in this box?

It cannot go in row 4 as there is already a 1 in row 4 column 4.

It cannot go in row 6 as there is already a 1 in row 6 column 1.

It must therefore go in row 5.

It cannot go in column 8 as there is already a 1 in column 8 row 2.

It must therefore go in row 5 column 7 as there is nowhere else for it to go.

This is called a hidden single in a box and the puzzle becomes: