Full Analytical Solution for Difficult KS on Friday 2/17/17

Here's the Full Analytical Solution for the Difficult Killer Sudoku on 2/17/17.

The starting puzzle:

**1)** F8-9 = [1,2]**2)** Using known values for columns H-I, H1+H7+H9 = 22. All must be 5+ and one must be 9.

**3)** The six-cell 23 cage at F6 is very telling. It must have 1-4 and cannot have a 9. 1-2 are blocked for F6-7 (from step 1) and H7 (from step 2).

**4)** With a 1-2 somewhere in G6-8, that blocks H9 from being 9, which means that

H1 = 9.

**5)** G1-2 must be [6,7] because [5,8] would block all answers for the 14 cage at G4.

**6)** All cells in the 28 cage at F2 must be 4+, so

G3 = [4,8].

**7)** Using known values for the G1-I3 block, H4 must be the same value as G3.

**8)** If both G3 and H4 are 4, then it would force G6 to be 8, which means that either H4 or G6 is 8.

**9)** With 8s and 9s blocked in the G4-I6 block, the 10 cage at

I4-5 must contain a 6 or a 7 and

I6 must also be [6,7].

**10)** With 6s and 7s blocked in column G and I,

H7,9 must be [6,7]. After clearing up a bit, we have:

It's honestly fairly easy from here on out.

**11)** With

[1,2,3] in G6-8,

F6-7 must be [4,7].

**12)** Using known values for the D7-F9 block, F7+D8 = 11, so

D8 must also be [4,7].

**13)** D-E9 must be [3,9] because everything else is blocked by G-H9.

**14)** E8 must be 6, and

D-E7 must be [5,8]. After some basic clearing, you have:

**15)** Using known values for the A7-C9 block, B6+D8 = 12, but B6 can't be a 5, so

B6 = 8 and

D8 = 4.

**16)** That means that

A7 must be 4, and after yet more clearing, we get:

**17)** Using known values for the D4-F6 block, D6+F4 = 15, but 8s are blocked for both, so

D6 = 9 and

F4 = 6.

**18)** B4-5 must be [1,6] because 2s and 3s are blocked.

**19)** A5-6 must be [3,9] because everything else is blocked by A7-8.

**20)** C5-6 must be [5,7],

C3-4 must be [3,4],

F2-3 must be [5,9], etc. etc. It's all easy from here.