I enjoyed this puzzle so much that I created some mini versions of it for fun. I signed up to share them with everyone. The rules are the same: Each region with n cells contains all the numbers from 1 to n and if two cells with the same number k are on the same row or column then there are at least k cells between them.
The answer:
1:
Order of solving: light blue, light green, orange, red, pink
2:
Order of solving: light blue, light green, orange, red, pink, dark blue, purple, brown, black, grey, yellow, dark green
3.
Order of solving: light blue, light green, orange, red, pink, dark blue, purple, brown
Green 2: the 2 in the top-right region must be in the right column. Then the 2 in the bottom-right region must be in the bottom row. Then the 2 in the + region must be in the centre.
Green 3: the only number that can go there.
4:
Order of solving: light blue, light green, orange, red, pink, dark blue, purple, brown
Light green 4: If the four was in the bottom cell of this region, there would be no place for the four in the bottom-left region.
Dark blue 1: The only number that can go there.
5:
Order of solving: light blue, light green, orange, red, pink, dark blue, purple, brown, black, grey, yellow
Light blue 3: if the 3 was on the right cell of the region, the bottom-right region couldn't have a 3.
Light green 4: If a 1 or a 2 was here, we wouldn't be able to place both a 1 and 2 in the central region bordering the bottom.
Orange 3: If the three was in the centre of the + region, we would have this:
and nothing could go in the top of the + region.
Red 2 and 4: Similar, if these were the other way around, we wouldn't be able to place anything in the top of the + region.
