r6c{8,9} and r{7,8}c2 must have the same color, and they can't be green, yellow or blue. Therefore, they must be red.

r{7,8}c8 must be green.

Two "X"s in box 1 must be green and blue.

The uncolored "X" in box 7 must be green.

Yellows and blues must be 2,8 and 3,7 in some order.

Let's consider where can 5 go in box 7.

• Either one of greens and reds is {4,6} pair, therefore, 5 can't be adjacent to reds and greens at the same time. Otherwise the 5 must be adjacent to 4 or 6.

• Now 5 can only be in r{8,9}c1.

• And we can determine the 5 in box 1.

The "X"s in box 1 is one green pair and one blue pair.

r1c2 and r2c2 are exactly one green cell and one blue cell.

Therefore, r9c2 must be a blue cell.

Furthermore, r9c2 is adjacent to 69 pair, so it must be 2 or 3.

r3c1 can't be green, can't be blue, can't be red, can't be 5, so it must be yellow.

And no matter which number it is, it must go to r7c3 in box 7.

In box 7, this yellow cell is adjacent to 14 pair, so it must be 7 or 8.

r6c3 could be 2378, but because of r7c3, now it must be 2 or 3.

And now, there is an interesting thing going on between green cells and blue cells.

• If green cells are 19 pairs, then blue cells must be 37 pairs.

• If green cells are 46 pairs, then blue cells must be 28 pairs.

That's use high vs low to disambiguate cells of the same color. Then we will have:

• Low green can't touch low yellow, and vice versa.

• High green can't touch high yellow, and vice verse.

• Low red can't touch low blue, and vice versa.

• High red can't touch high blue, and vice versa.

• 5 can't touch red and green at the same time.

• 5 can either touch red or green, but not both, and the this must be consistent on the entire board.

Where can yellow 78 (or high yellow) go in box 9?

• It can't touch green 69, so it must be on row 9.

Now, the "X" in box 8 can't be blue, can't be green, can't be yellow (because of yellow 78 in box 9), so it must be red.

Now the "X" in box 9 can only be yellow, and we know which is high and which is low.

There's only 1 place for green 14 in box 8.

There's only 1 place for red 69 in box 9.

In box 9, 5 can't go to r7c9, r8c7.

Now we know that 5 must touch a green cell. And we now know the mapping of each color:

• Green ==> 19

• Yellow => 28

• Blue ==> 37

• Red ==> 46

Let's update all pencil marks.

Now we have used all the "X" "V" constraints.

It's just a nonconsecutive Sudoku now.