This is the author's algorithm; other players are more than welcome to contribute to additional solutions.

Lovely explanation Chen Cen.... However, when I solved, I deviated from step 7 onwards... Steps 1 to 6 are exactly as you explained... I will continue from step 7 onwards an alternate route to solve this....

--------------------------------------------

R9C5 has to be an odd number since the 4 is in R7C5 and no other even number can precede it .... 1,5,9 are eliminated due to normal sudoku rules... 7 has to be a part of R8C6 or R9C6 since R6C6 is a 9 and no odd number can precede 7 in column six via the constraints of box 8. Hence R9C5 is a 3. Similarly 2 has to be in R9C4.






Attachments
----------------
OStep7.png (32KB - 1 downloads)

Now in Box 9, the numbers 8 and 9 are in R7C7 or R8C7 or R9C7.... this allows for a naked single 7 in R9C8. Based on this we fill up the 8 and 9 also in Row 9. R9C6=8 and R9C7=9.

Entire Box 9 can be filled now. R8C7=8, R7C7=3 and R8C8=4 by normal sudoku rules. This allows for R7C8=6 as per constraints of Box 9 and finally R8C9=5.





Attachments
----------------
OStep8.png (36KB - 0 downloads)

Again based on normal sudoku rules, we also fill up the entire Box 8.

R7C4=9, R7C6=5, R8C6=7, R8C4=6.







Attachments
----------------
OStep9.png (37KB - 0 downloads)

Now in Box 6, the middle row has a sum of 22 which can only be either 9,6,7 or 9,8,5. since 6 and 7 are already present in Column 8, the middle row has to be 9,8,5.

By normal sudoku rules, R5C8=8,R5C7=5,R3C8=5,R4C3=8, R4C8=2.

By constraints of Box 4, R5C1 has to be a 7.





Attachments
----------------
OStep10.png (40KB - 1 downloads)

After step 10, since all external constraints are satisfied, the present grid can be solved logically as any other classic sudoku.

Hope this was helpful.

Rishi (purifire)

Thanks cpickerel and Rishi for the detailed writeup with images.

RJH0723, hope that was useful to you.

Thanks Guys. That helped a lot. The key thing I missed was the R6 skyscraper constraint. That would have enabled me to finish it. You guys are the best!

Glad this was helpful....

Rishi