# Solutions to Race up the Sky – 2/4

Puzzle 3 –  Skyscraper Sudoku
The Sudoku was the first to be made and the last to be completed. I wrote this in April, expecting it to be moderately hard, and at the end of May, when I was test solving, I couldn’t remember my own solving path! I tried adding extra clues to the point that I got very bored and frustrated with my own puzzle. If I, the constructor, got sick of it, then it couldn’t be good for my readers. I scrapped half of my grid and end up with this puzzle.

The solving path is quite narrow, after adding trivial 9s and 8s; you then need to recognize the high skyscrapers clue to restrict your placements.

Now take a look at the first column and the top left region. 3, 4, 5 and 7 are missing and the first column indicates that 4 buildings should be seen. Possible candidates for the C1R2 cell are 4 and 5. 7 can’t be there otherwise you won’t get 4 buildings seen, so 7 will be seen after the 6 and before the 9. You will need to have one more building seen, so if C1R2 is 5, C1R1 cannot obscure the 5 and will see more than 4 buildings. Conclusion: C1R2 is 4.

The next break-in is at the last column. You can see that 6 can only take the C9R6 cell. Staying on the same column, 5 can only be on C9R3 since putting 5 on C9R9 requires a 6 to be seen before the 7 which is impossible.

Even when there were a little more than 10 cells left, the solving still isn’t easy. Every clue and every given had to be used to squeeze out the answer. Lastly, look at C9R9. Filling it with a 3 will have you solving the sudoku for 5 or so more cells to see that it is invalid. You would have to come back and fill C9R9 with a 4 for the puzzle to be completed correctly.