Before we start solving, there's a few logical deductions we can make at the very start:
- For Green, a 6 or a 4 can only ever be on the ends (assuming the two adjacent cells 'see' each other), or the two adjacent cells will have the same value
- Green can also never contain a 5 as no number is 5+ away in sudoku
So with this basic information, we can start trying to narrow down the candidates, and hopefully placing some numbers.
For all images, click/open link for a larger, clearer version - otherwise images are very large
1. Placing candidates
The obvious first step is a 9 must be next to the 4. After this, there are no obvious numbers to place, but the majority of the green lines only can have certain candidates in each cell, or other cells along the line will be impossible to fill. Not too much to show here.
2. A breakthrough!
Consider the 7th column. The 8 in this column can only go in the 2 highlighted cells, as it can not be part of the purple line. Now looking at the green line, with all 8s removed, the top of the green must be 2/3 as a 9 would need another 9 in the square. This places quite a few numbers, including the 8!
3. Moving on to purple
Look now at the purple line bottom right. It is only 3 numbers, but it is actually has to be 5-6-7 or the green above in the same column won't have any candidates. There is obviously now a triple, and this means there must be an 8 in the aforementioned green. This leaves only a 4 in the column, top right. The last bit step here, is there now must be a 8 in the bottom right green, as its the only place an 8 can go in that column:
4. The big cane gives one
There is one obviously larger cane - a purple of length 9. This must contain all the numbers from 1-9 in some order. There is already only one place an 8 can go, and this solves the green in the same column, and this in turn places some numbers in the big green cane - a nice flow of placements! The final bit of logic is to see that a 1 must be in the bottom left of the big cane, which removes some candidates to the right and places a 6.
5. The flow of candy
This puzzle is beautifully made in the such that you place one number and it opens the door to the next, and the solution flows very nicely. The last 6 placed solves a couple of numbers in the green cane in the same row. As there is a 1-5-7 in row 7, this places the 9 in column 1. Now consider the purple middle right. It cannot be 2-3-4 or R9C7 has no candidates. So the purple must be 3-4-5 or 4-5-6. Either way, there is a 5, which fixes a 1 in the column and places multiple other numbers.
6. An unused purple
Consider the purple top left. It must be 3-4-5-6 as it cannot contain 2 and 3 or the green to the right has no candidates. 4 can then only go in one place, and a 2 and 8 is fixed to the right. This dominoes around the grid placing a few other numbers as a result. A considerable portion of the board is now filled and we can almost solve.
7. Major progress!
This stage can now be reached with some normal sudoku logic. The next breakthrough is to look at the small 3-purple top left. It can be a 2/8 in one cell so this reduces the triplets it can be. However if it has a 2, it must be a 1-2-3 or a 2-3-4, neither of which is possible. It must be an 8, and a 6-7-8 or 7-8-9. Either way, a 7 is used created a pair of doubles in row 1 and 2, placing a 7 at the bottom of row 3. There is also only one place for 8 and 1 to go middle left.
8. The last breakthrough
The final breakthrough here is to look at row 9 column 6. If it is 4, or 5, then there is no where for 4 or 5 on the large purple cane. So it must be a 9. The rest of the numbers all fall into place with normal sudoku logic.
The solution:
Great puzzle! Had a lovely flow to it while still being very difficult :)
