## six box quicky

All about puzzles in newspapers, magazines, and books

### six box quicky

Hi. I've got this tiny puzzle here, that I can't seem to solve without trial and error. Can anyone see the natural way out? Thanks.

x12 x5x
3x5 1x2

xx1 xxx
xxx 2xx

1x3 5x6
x5x 3xx
noggi

Posts: 11
Joined: 26 July 2005

I wouldn't go so far as to call the following natural but hopefully it will be of help. It's the simplest solution I could coax out of my solver:

Code: Select all
`1. The cell r1c6 is the only candidate for the value 3 in Row 1.2. Consider the chain r2c5-4-r2c2~4~r5c2-4-r5c5.The cell r5c5 must contain the value 4 if the cell r2c5 doesn't.Therefore, these two cells are the only candidates for the value 4 in Column 5.- The moves r3c5:=4, r4c5:=4 and r6c5:=4 have been eliminated.Consider the chain r2c2-4-r2c5-4-r5c5-4-r5c2.The cell r5c2 must contain the value 4 if the cell r2c2 doesn't.Therefore, these two cells are the only candidates for the value 4 in Column 2.- The moves r3c2:=4 and r4c2:=4 have been eliminated.Consider the chain r3c2~6~r2c2-6-r1c1-6-r1c4-6-r3c4.When the cell r3c2 contains the value 6, so does the cell r3c4 - a contradiction.Therefore, the cell r3c2 cannot contain the value 6.- The move r3c2:=6 has been eliminated.Consider the chain r3c1-2-r6c1-6-r6c3-4-r4c3~4~r3c1.When the cell r3c1 contains the value 4, it likewise contains the value 2 - a contradiction.Therefore, the cell r3c1 cannot contain the value 4.- The move r3c1:=4 has been eliminated.The value 4 in Box 4 must lie in Row 3.- The move r4c6:=4 has been eliminated.Consider the chain r6c1-2-r3c1-5-r3c6-4-r6c6~4~r6c1.When the cell r6c1 contains the value 4, it likewise contains the value 2 - a contradiction.Therefore, the cell r6c1 cannot contain the value 4.- The move r6c1:=4 has been eliminated.Consider the chain r2c2-4-r5c2-2-r6c1~6~r1c1-4-r2c2.When the cell r2c2 contains the value 4, the chain is self-contradicting. Therefore, the cell r2c2 cannot contain the value 4.- The move r2c2:=4 has been eliminated.The value 6 is the only candidate for the cell r2c2.`
Sue De Coq

Posts: 93
Joined: 01 April 2005

Thanks. I thought some sort of chain was needed.
noggi

Posts: 11
Joined: 26 July 2005

I don't have a solver -- here's a paper based solution. This is a good example of why these 6x6 puzzles are so good to work on. More complex tactics are much easier to spot, especially when solving on paper, than in a 9x9.

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`+------------------+------------------+|  .     1     2   |   .     5     .  ||  3     .     5   |   1     .     2  | +------------------+------------------+|  .     .     1   |   .     .     .  ||  .     .     .   |   2     .     .  |+------------------+------------------+|  1     .     3   |   5     .     6  ||  .     5     .   |   3     .     .  |+------------------+------------------+`

Tactics in the order I found them:

(1) Filling in r1c6=3 (single) and the candidate lists:
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`+------------------+------------------+|  46     1     2  |  46     5     3  ||   3    46     5  |   1    46     2  |+------------------+------------------+|2456  2346     1  |  46   346    45  || 456   346    46  |   2  1346   145  |+------------------+------------------+|   1    24     3  |   5    24     6  || 246     5    46  |   3   124    14  |+------------------+------------------+`

(2) Coloring 6s eliminates the candidate 6 from r3c2:
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`+------------------+------------------+| +46     1     2  | -46     5     3  ||   3   -46     5  |   1    46     2  |+------------------+------------------+|2456  234x     1  | +46   346    45  || 456   346    46  |   2  1346   145  |+------------------+------------------+|   1    24     3  |   5    24     6  || 246     5    46  |   3   124    14  |+------------------+------------------+`

(3) X-wing in 4s, rows 2 and 5, eliminates candidates 4 from r34c25:
Code: Select all
`+------------------+------------------+|  46     1     2  |  46     5     3  ||   3   +46     5  |   1   +46     2  |+------------------+------------------+|2456   23x     1  |  46   3x6    45  || 456   3x6    46  |   2  13x6   145  |+------------------+------------------+|   1   +24     3  |   5   +24     6  || 246     5    46  |   3   124    14  |+------------------+------------------+`

(4) No xy-wing exists. There is at least one forcing chain in the five marked (+) cells:
Code: Select all
`+------------------+------------------+|  46     1     2  |  46     5     3  ||   3    46     5  |   1   +46     2  |+------------------+------------------+|2456   +23     1  |  46   +36    45  || 456    36    46  |   2   136   145  |+------------------+------------------+|   1   +24     3  |   5   +24     6  || 246     5    46  |   3   124    14  |+------------------+------------------++------------------+------------------+|   .     .     .  |   .     .     .  ||   .     .     .  |   .    46     .  |+------------------+------------------+|   .    23     .  |   .    36     .  ||   .     .     .  |   .     .     .  |+------------------+------------------+|   .    24     .  |   .    24     .  ||   .     .     .  |   .     .     .  |+------------------+------------------+`

Either value for r2c3 leads to r5c2=4.

The rest is relatively simple.
tso

Posts: 798
Joined: 22 June 2005