In this puzzle, we have put as many numbers in the upper parts of
the squares. Notice in the UL box
where the red arrow is pointing. The five squares with numbers
1,3,7,8,9 are all "joined" and "lock" up
those squares. There is only one number left missing from that
box ... the number 2. So it must go
into the top left square. We would not know that if we had not
been putting numbers in the top of
the squares.
Also notice in the UR box the two empty squares. The 2 and
5 have two of the squares locked up.
The only two numbers missing are 4 and 6. They have to go into
the two empty squares and the 4 goes
into the top square because of the 4 in the UM box. The 6 goes
below the 4. See the second picture
with the red letters.
Then watch what happens to the 6 and 9 in the squares to the left.
Then the green 9 in the UM box tells where the 9 is in the UL box.
Then the blue 3... 1... 8.... and 7 follow.
Now we are well on the road to finishing this puzzle. Only when
you put the numbers in the top of the squares.