SudokuSolves/RiverRun

https://f-puzzles.com/?id=yf84zu6b

Step 1 : Node at Row 8 Col 1-2

45 - 8 - (1-9) = somewhere between 28 and 36

Step 2 : Node at Row 7 Col 4-5

4 digits in a row (Row 8 Col 4-7) have a max of 30 and a min of 10 but there's no "0" digit, so 11 - 29

But we know the second digit must be 9, from r2c6 and r5c7

Step 3 : Node at r9 c8-9

8 + ( 19 or 29) + (28 to 36) = ?8

For that to balance, the last digit of Row 8 Col 1-2 must be the digit "1" which makes that node 31

45 - 8 - 31 = 6 so the bottom right corner node must be 68, making the bottom middle node 29.

To double check:

31 + 29 + 8 = 68

https://f-puzzles.com/?id=y4govep8

Step 4 : Killer Cage sums

Pencil in the possibilities for the pipes on row 8 and 9, column 8, and the "2" at r6c6

https://f-puzzles.com/?id=yyb336u4

Step 5 : Singletons

r8c7 must be a 9 (only place on the pipe for it)
r4c2 must be a 2 (31 - a single digit)
r7c6 = 6 (sudoku)
r8c3 = 6 (sudoku)

Step 6 : Box 4

Length 2 arrow with no digit "2" or "3" is a minimum of 5
Which makes the node on row 4 a max of 26 (but 6 is not possible, so 25)
Minimum is 21, but that still makes the pipe from it have only "4" or higher.

Step 7 : Matching nodes

5/6/7/9 + 1/3/4/5 = 11
valid pairs are: 6+5, 7+4

1/4/5 + 4/5 = 6/7
valid pairs are 5+1 = 6

That puts 25 in the other node, and the only way to make it in 3 cells is 8,8,9

Step 8 : the 8 pipe in box 6 and box 9

8 = 2/4 + 1/3 + 3/4/5
Valid combos are: 2+1+5 or 4+1+3

https://f-puzzles.com/?id=y2hglb5z

Step 9 : Box 1

r2c1 is 4/8/9
r3c2 is 3/4/5/6/7/9
Which would leave r1c2 as minimum 7
However we can also eliminate any combo that adds to more than 9
Valid combos = 4+3=7 and 4+5=9

Which makes the other node 25 - (7 or 9) = 16 or 18

https://f-puzzles.com/?id=yxkdj42w

Step 10 : Box 1 & 2 zig zag pipe

r2c3 is a naked singleton "3"
making r3c2 "5", r1c1 "9" and r1c4 "6"

This results in the pipe being 8/3/3/2

https://f-puzzles.com/?id=y2g38d2e

Step 11 : Straight sudoku

We can fill in most of the left side now:

https://f-puzzles.com/?id=y5jodyl7

Step 12 : the length 4 pipe in box 5

Looking at valid combinations, we get from the top down:

9+8+(3/4/7)+(3/6/7)

Step 13 : row 8 in box 8

The 7 and 8 in column 6 give us r8c6 as "5" which resolves that triple.

This in turn bounces up and resolves box 2

Step 14 :

Box 3 naked singles:

r2c7 = "1"
r1c7 = "8"
r3c8 = "7"

Pencil mark in the rest:

https://f-puzzles.com/?id=yye4yfup

Step 15 : THE TRICKY STEP

Have a look at the highlighted cells:

https://f-puzzles.com/?id=y28a5cot

If you put a "4" in r5c5, it puts "3"s in both the pink and yellow cells, which in turn eliminate "3" from the red and gold cells in box 5.

REMEMBER TO REMOVE THE "6" from r6c5 (this is the tricky bit)

In row 5 and 6, the "3" must be in c2 or c5 so you can remove the "3" from r6c8

https://f-puzzles.com/?id=y4fuk849

Step 16 : Straight sudoku

https://f-puzzles.com/?id=y54pmyhg