There is actually a combination of relatively easy patterns behind this puzzle. I think the first thing we all should notice is the number of shaded blocks:
The first picture has 1.
The second one has 2.
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The third one has 3.
And so on. So that’s the first pattern established.
Next. notice how the are filled. Picture one starts filling from diagonal 1, which is the top-right diagonal.
Picture two, the 2 shaded blocks are on the second diagonal.
Picture three, 3 shaded blocks on third diagonal.
Now picture 4 gets interesting. The pieces start from 4th diagonal since in pattern 3 we have filled up until 3rd diagonal, but only 2 pieces can fit in, and pattern 4 has 4 in total! So another 1 piece moves down to diagonal 5 and the last one restarts at 1st diagonal. In summary:
first 2 pieces — 4th diagonal
next 1 piece — 5th diagonal
Last 1 piece — 1st diagonal.
It’s the same for pattern 5. Starting diagonal of 2 since pattern 4 ended at diagonal 1, and then pieces get carried over to next diagonal after one diagonal is filled up.
So pattern 6 would have a starting diagonal of 4 (pattern 5 filled up to 3) and pieces arrangement as follows:
Fist 2 pieces — diagonal 4
Next 1 piece — diagonal 5
Next 1 piece — diagonal 1 (restart)
Last 2 pieces — diagonal 2
To help you visualise this pattern, you could think of someone painting the blocks diagonally, but in different sets, Pattern 1 represents the first 1 block he paints, then, say, he takes a rest, continues painting where he left off, and this goes on. When he has finished painting one 3×3 block, he moves on to another block.
(Here you see the pattern. The lighter-coloured blocked denote the blocks the painter starts on first.)