15
$\begingroup$

Fill each empty cell of the board on the left with a digit between 1 and 9. Each box and each column and row must contain all digits.

The dots outside the board on the right indicate how many cells in the corresponding column or row of that board contain precisely the same digit as is to be found in the same cell on the board on the left. (Puzzle by Xavier Castillo)

enter image description here

$\endgroup$

1 Answer 1

13
$\begingroup$

Solution:

enter image description here


Step by step:

1 - Back to basics:

To start, there is only 1 cell that can be filled with normal logic, a 2 in the first box. So clearly the focus should be on the paired grid, and some cells can be highlighted that match/don't match to help with deductions. We also have a row with 0 dots, so there are no matches in that row either.

enter image description here

2 - Impossible placements:

We can also mark a lot more cells as red if they cannot be placed in the left grid due to normal sudoku rules of clashing with another number in a row/column/box.
The middle column is now 'complete' - all cells are red except for 3 remaining cells, which matches the number of dots - so these cells must match the left grid and can be placed:

enter image description here

3 - Seeing double:

Now several row/columns are almost complete, but may have one more remaining cell than there are dots. However, some also contain multiple of the same number.

Consider the top row. Right now, there are 7 remaining cells, but 6 dots - but there are also 2 6s in the right grid. Only one of these 6s can be green and the other must be red, which means all the other cells must be green and can be placed.

This can be applied to R1, R4 and C2:

enter image description here

4 - Scratched out:

C8 and C9 are both now complete, so the remaining cells can be filled red. Repeating the process of filling in cells on the right red if it now cannot be placed on the left due to normal sudoku logic also completes C7, and completing column 7 in turn completes R5.

enter image description here

5 - Pairing up:

We can now apply some normal sudoku logic and place a 2 in the 6th and 9th boxes (naked singles). There is now a 1/5 pair in the 6th box, which means on the right grid 1 and 5 can be marked red across the rest of the 6th row and the 6th row is then completed.

This in turn completes C2 which then completes R9, placing a 4. C4 is then almost complete and 3 more numbers can be placed, which also completes R1.

enter image description here

6 - The Old Fashioned Way:

With so many numbers now placed on the left, lots of normal sudoku logic can be applied and a good portion is filled out. There are a lot of naked singles, and from that logic alone, we can reach the following (note right grid not updated):

enter image description here

7 - Finishing touches:

Updating the right grid will let us finish off the puzzle. R7 and C1 are the major giveaways, as they are both complete and allow cells to be filled to solve the remaining pairs in the left grid, giving the final solution:

enter image description here

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.