Step 1
The three digits in Row 6 have sum 8, so they can only be 125 or 134.
Using the skyscraper information on the left and the sum information
on the right we can deduct the above four digits for Row 6. The 9 in
Row 4 can also be deducted directly from the skyscraper information.
Step 2
According to the requirement for Column 6, the closest odd digit to
the bottom is 7, and the distance between 9 and 1 in this column is 3,
therefore R3C6=1. Since the sum of all digits between 1 and 9 in Row 3
is 0, and 9 in Column 7 is in Box 9, so R3C5=9. Then
Step 3
Now all digits in Box 7 can be deducted. With the information outside
Boxes 8 and 9, we have R7C5=4, R7C9=2, R9C9=1.
Step 4
Back to the skyscraper in Row 6. With the 6 we know R6C1
R6C1={23}. R6C1 and R8C1 is a naked pair of {23}. Thus in Column 1
R1C1 can't be 2, R2C1=1. Since the sum of all digits between 1 and 9 in Row 2
is 27, and in Column 7 the digit 9 is in Box 9, R2C8=9, R2C9=8.
Step 5
With the information for Row 1, the distance between 1 and 9 should be
6 or 7; since there are already 1’s in Columns 1 and 9, R1C2=9,
R1C8=1. R1C1+R1C9=7. And since there are 1’s and 2’s in Columns 1 and
9, and 3 in Column 1, R1C1=4, R1C9=3.
Step 6
According to the information outside Column 2, we have R4C2=3. All
digits in Row 6 can then be deducted.
Step 7
Using standard Sudoku algorithm and the information outside Box 9, we
have the above digits.
Step 8
With the information for Box 8 Column 4, R9C4=2.
With the sum requirement for Box 6, R5C7+R5C8+R5C9=22. Using the known
digits in Box 9, we have R5C7=5, R5C8=8.
The rest can be solved using standard Sudoku algorithm.
sneaky trick
On the other hand, a sneaky trick can be applied at the beginning:
Following Step 1, using the information for skyscrapers, R6C1=2,
R6C2=5, or R6C1=3, R6C2=4.
With the information for Column 2, either R3C2=4, or R4C2=3. No matter
which one holds, R6C1=3 and R6C2=4 will lead to contradiction. Thus
R6C1=2, R6C2=5. The algorithm can then be continued by applying
information for Column 1.