Sunday, 7 December 2014

grid deduction - Unusual Sudoku Puzzle


Find the solution to this Sudoku puzzle. The only problem is there aren't any normal Sudoku clues. Instead there are only some cryptic clues.


Puzzle Image



What is the solution and how does the puzzle work?


Edit: Now that it is solved, I want to give my inspiration for this puzzle. It gives away part of the answer, so don't look unless you want a hint.



I got the idea for the nonogram part of the puzzle from Sligthly Odd Sudoku. This is still an unsolved puzzle, so take a look at that one if you liked this one.




Answer



The first thing to do is



look at the top and left clues. These form a nonogram / Picross puzzle, which has this solution:

enter image description here




Next,



the bottom and right clues. In all the places where there are two groups of shaded cells, there is only one number, and vice versa. This suggests that the groups of empty cells are relevant -- in fact, the unshaded cells in the center form the grid for a Kakuro (Cross-Sums) puzzle! Keeping in mind the additional constraint that numbers can't repeat anywhere within a row, column, or box (even if blocked by shaded cells), this can be solved as follows:

kakuro step 1 kakuro step 2 kakuro step 3
kakuro step 4 kakuro step 5 kakuro step 6
kakuro solution



And finally, the Sudoku can be solved:



sudoku step 1 sudoku step 2 sudoku step 3 sudoku step 4
sudoku solution




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