# Bulls and Cows meet Sudoku!

This is a Colombian Jigsaw Sudoku where the usual rules apply, but with irregular boxes. The dots in the right-hand scheme indicate how many of the numbers in a particular row or column are correctly placed in the corresponding row or column of the solved Sudoku on the left.

• SudokuPad link for interested solvers: tinyurl.com/55vn8y59 No warranty expressed or implied. Commented Jun 24 at 20:26

The final grid:

Starting with matching, we can:

Shade red any cell that cannot possibly be a match, and shade blue any cell that is definitely a match. Just based on the initial position of the grid, we get:

Initial analysis:

We first look at rows/columns where the number of matches or non-matches is close to the needed amount. So in row 3, we need four matches, and have only five possible cells which could match: columns 1,2,3,6,7. Columns 3 and 7 are already matches, so two of columns 1,2,6 must match. But column 2 and column 6 cannot both match, as they would both need a three, so column 1 must be a match, forcing R3C1 to be a 5. Similarly in row 8, we need three more matches from two 8s, two 4s and a 6, so the 6 in R8C3 must be a match. The same analysis in row 9 shows R9C3 is 5. And in column 8, we get two digits R1C8 = 7 and R4C8 = 3. The grid thus far:

A little bit more subtle:

In row 9, we must have 3 matches. We already have a 5, so the others must be a 4 and a 6, and both are in the long skinny region at bottom. In particular, this means R8C5 is not 4, which means this cell is not a match. But now in R8, we must have two more matches, one of which is an 8, and the other of which is a 4. This forces R8C1 to be a 4.

And a little less subtle:

I always forget that a row without dots means there's no match, not that a clue is absent. So we know all cells in R6 are not matches.

Let's do some sudoku:

We've got a lot of given 7s, so the irregular geometry helps us. The twisty region containing R7C9 has only one possible place for 7, so R6C9 is 7. Now the only place for 7 in column 1 is R5C1, which forces R8C4 and R9C5 to be 7s as well. Now looking at match logic in row 9, we must have R9C4 = 4. We now know there are no other matches in column 4. The grid thus far:

Some more match logic:

In row 8, the 9 must be in column 7 or 9, which means R7C6 cannot be a 9, and is thus not a match. In column 5, we need three matches from two 5s, two 6s and a 9, so the 9 in row 1 must be a match.

Seeking 9:

Where can the 9 go in row 6? It cannot be in columns 1,4,5,6,9 by sudoku. Moreover, it cannot go in columns 7 or 8, since that would give matches in a row that has none. So the 9 must be in columns 2 or 3, which are in the same region. This means that R7C2 cannot be a 9, which means this cell is not a match.

R5C3 also cannot be 9. If it were, then in column 3 R5C3 would not be a match since it's not 3, and R4C3 would not be a match, since it could not be 9, so column 3 would have at most 5 matches. R5C4 is not 9 since it would be a match in a column that needs no more, so we must have one of R4C2 or R4C3 as 9. Now by sudoku, one of R3C4 or R3C6 must be 9, as must one of R5C6 or R7C4, as must one of R5C7 or R7C9. Hmm, that didn't do as much as I hoped. The grid thus far:

Ah...column 2:

Needs two matches, which forces R4C2 to be 9, and thus R6C3 as well. Now row 4 has its two matches, so R4C5 is not a match. Since column 5 needs three matches, R5C5 must be a 5.

And back to column 3:

Placing the 9 in R4C2 forces R4C3 to not be a match, which means R1C3=8 and R5C3=3 must be matches. Now R5C2 is not a match, which forces R3C2=3 to be a match. This fills up all of row 3s matches.

Another hit of sudoku:

R1C7 is the only place in the upper right region that can have a 3. Now we can pencilmark row 1, and find that R1C2 is 4. This resolves all digits in column 3. Moreover, we now have four matches in row 1, so R1C6 cannot be 1, resolving all digits in the row. The 5 in R1C6 means R2C6 is not a match. R2C5 must be 6 to fill the region, making it a match. We now have 3 matches in column 5, so R7C5 is not a match, forcing R7C9 to be a match, which resolves all the 9s.

Back to matching logic:

Row 9 now has all of its matches, so R2C9 and R5C9 are not matches. This forces R2C7 to be a match (4), R5C7 to NOT match, R9C7 to match (6), R9C6 to NOT match, and R8C6 to match (8). We now have all of our matches/not matches mapped. The grid thus far:

Finishing up with sudoku:

Column 4 resolves immediately, and places a 2 in R6C5. Row 6 now needs 1/3/5/6; R6C& and R6C8 cannot be either 1 or 3 by the region, so they are 5/6, which resolve. The 1/3 resolve in columns 1 and 2. Column 7 leaves a 2/8 pair, which resolves. Row 5 needs a 1/4/6; the region forces R5C2 to be 6. Column 2 needs a 2/8 pair, which resolves by the bottom region. The rest is pretty straightforward fill.