Filling numbers in a grid

Here's the problem and the diagram that goes with it

Fill in each empty space of the grid in the image below with a number from 1 to 8 so that every row & column contains each of these digits only once. Some diagonally adjacent spaces have been joined together. For these pairs of joined spaces the same number must be written in both.

Diagram:

A substitute teacher provided us with this puzzle. Can you please provide an explanation of how to get to the answer?

• Welcome to PSE! This looks like a neat puzzle...did you write this puzzle yourself, or is it from another source? Community guidelines require attribution if you did not write the puzzle yourself. Oct 19, 2020 at 20:29
• @JeremyDover The original post attributes it to a substitute teacher, but this was edited away Oct 19, 2020 at 20:36
• @JeremyDover I originally wrote that this was from a substitute teacher, but someone else edited it out. Oct 19, 2020 at 20:37
• This puzzle type is known as Staircases on Puzzle Picnic. Oct 19, 2020 at 23:40

The solved grid:

And here's how to solved it:

STEP 1:

Look at the conjoined cells on the right at the bottom. These are 'seen' by all numbers except 6, so must be 6. This fixes 6s in the bottom left, meaning three other conjoined cells are 'seen' by all but 1 number, which we can then place.

STEP 2:

Look at the ones. All the ones can now be placed through normal rules. This then allows us to fill out some rows/columns and hence place a few others through deduction.

STEP 3:

Now look at the sixes. These can all be filled in. Filling in certain rows allows us to place numbers where we had two candidates, as one of the pair is ruled out.

FINAL STEP:

From here, the rest of the cells can be filled in simply by looking at what remains in each row/column and voila!

• Just beat me! :-) Nice solve... Oct 19, 2020 at 21:02
• @JeremyDover was quite fun once you got going! Sorry for sniping you :P Oct 19, 2020 at 21:03
• Agreed. It felt like a trudge at first, but then you hit the neat deductive steps. Oct 19, 2020 at 21:04
• Thanks for the in-depth answer @BeastlyGerbil Oct 19, 2020 at 21:08
• @Aayush no problem! Hope this helped Oct 19, 2020 at 21:35