triple5

prev ----------------------- contents ----------------------- page030 ----------------------- next

  Higher order circles.

  Circles of length 4, 5, 6, even 7 
    are common in difficult puzzles.
    
  They usually do not lead to deductions.

  Example from POK Journal 060408 Six Light Stars.
    (Notice the skinny, 2x4 circle in column 2.)
       1         2         3          4         5         6          7         8         9       
  .---------.---------.---------..---------.---------.---------..---------.---------.---------.  
a |         |       89|       89||         |         |         ||         |         |         | a
b |         |         |         ||         |         |         ||         |         |         | b
c |         |         |         ||         |         |         ||         |         |         | c
  |---------+---------+---------++---------+---------+---------++---------+---------+---------|  
d |  3  6   |    5 7  |    5 7  ||         |         |         ||  3  6   |         |         | d
e |  3    89|         |  3    89||         |         |         ||  3     9|         |         | e
f |         |         |     6  9||         |         |         ||     6  9|         |         | f
  |---------+---------+---------++---------+---------+---------++---------+---------+---------|  
g |     6 8 |    5  8 |    56 8 ||         |         |         ||         |         |         | g
h |         |         |         ||         |         |         ||         |         |         | h
i |  3     9|      7 9|  3   7 9||         |         |         ||         |         |         | i
  '---------'---------'---------''---------'---------'---------''---------'---------'---------'  
       1         2         3          4         5         6          7         8         9     

    digits  3 5 6 7 8 9 | possibilities
           ------------ |  
    cells           8 9 | 8 8 8 9 9               
              5   7     | 5 7 7 5 7                
            3       8 9 | 3 3 9 3 8                
                6     9 | 9 6 6 6 6                
              5 6   8   | 6 5 5 8 5                
            3     7   9 | 7 9 3 7 3           

  Check that every row of possibilities contains
    every digit in the corresponding cell.

  Check that every column contains every digit.  It does.
  
  I can't deduce anything from this.