The numbers 1 to 9 are to be placed once in every row, column, long diagonal, 3x3 grid and irregular shape (or cage). From the given starters can you complete the puzzle?

By hand, using logic, I was able to get as far as:

84        5 1
172       48
 35        2 
   
  3  1 5  248
52   84   163
481  236   5 
  
 1     8  374
     3    895
358       612

I entered the above into a regular sudoku solver program I had written, and it came up with two solutions using ordinary sudoku rules, one of which was valid for this Logidoku:

 8 4 6  9 2 7  5 3 1
 1 7 2  6 5 3  4 8 9
 9 3 5  4 8 1  7 2 6


 6 9 3  1 7 5  2 4 8
 5 2 7  8 4 9  1 6 3
 4 8 1  2 3 6  9 5 7








 2 1 9  5 6 8  3 7 4
 7 6 4  3 1 2  8 9 5
 3 5 8  7 9 4  6 1 2

The alternate ordinary-sudoku soln had the 6's and 5's interchanged in columns 4 and 5, rows 2 and 7, which doesn't work here due to the color areas in the upper-left and upper center.