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How to play Killer Sudoku-X

Killer Sudoku-X is a straightforward combination of Sudoku-X and Killer Sudoku. In other words, it is Killer Sudoku with the additional constraint that each of the two main diagonals must also contain each of the numbers 1 to 9 (or 1 to whatever the width of the puzzle is) .

In Killer Sudoku-X you must place each of the numbers 1 to 9 (or the width of the puzzle) into all of the rows, columns, bold-lined boxes and each of the two main diagonals (shaded in pink on puzzlemix). Additionally, however, you must also place the numbers so that each dashed-line 'cage' adds up to the total given at the top-left in smaller digits. For example, the three squares at the bottom-right corner of this puzzle inside the '7' cage must add up to 7. You also cannot repeat a number within a cage, so this means for example that the solution to '7' over three squares can only be 1 and 2 and 4, not any other combination such as 1 and 3 and 3 (although in this particular case two 3s would break the normal rules of Sudoku in any case).

By marking some of the 'only fit' numbers in as pencilmarks we can start to solve the puzzle. For example in the right-most column we can mark in the 1, 2 and 4 for the '7' cage as well as an 8 and 9 in the '17' cage. If we then begin marking in the remaining fits for some more of the cage we can start to progress:

These marks are very important in killer sudoku x. For example in the bottom-right 3x3 we can now see that the number 3 can only fit in the '14' cage; this lets us eliminate it from the '12' cage four squares above the blue shaded square - and so we can place two numbers:

Via a simple 'ripple effect' of eliminations we can in fact solve a total of three cages, as shown. And then using further notes and eliminations we can continue to solve the rest of the puzzle. Logic alone is all that you need to solve every killer sudoku-x puzzle! There is never any need to guess.

Continue to solve the puzzle using both regular Sudoku and Sudoku-X logic and a range of possible deductions unique to Killer Sudoku/Killer Sudoku-X, and you will eventually reach the final result. When the puzzle is fully-solved you will have 1 to 9 in each row, column, 3-by-3 shape and two main diagonals, and each cage will add up to the total at its top-left:

Once you get really good at Killer Sudoku-X, you might even find you can solve some of them faster than standard Sudoku or Sudoku-X!

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