## Solving a hard one

All about puzzles in newspapers, magazines, and books

### Solving a hard one

As a compensation for the bad sample last time i want to show, how a pretty hard sudoku can be solved. Its nr 149 from the outlaws in the sudoku gallery.
Of course i know, there are many other ways to solve it (just looked at rubylip, says "The move (2,5):=3 would lead to a contradiction.."), but the steps might be interesting for others.

Code: Select all
. . 1 | . 5 . | . . 2
6 . . | 4 . . | . . .
. 9 . | . . . | 3 . .
----------------------
. . 8 | . . 7 | . . 1
. . 5 | 6 . . | 4 . .
2 . . | . . . | 9 . .
----------------------
. . 7 | . . . | . 8 .
. . . | . . 3 | . . 5
4 . . | . 2 . | 6 . .

The first time i got stuck here:

Code: Select all
378   3478   1      3789   5       689     78   4679  2
6     23578  23     4      13789   1289    1578 1579  79
578   9      24     1278   1678    1268    3    14567 467

39    346    8      2359   349     7       25   2356  1
1379  137    5      6      1389    1289    4    237   378
2     13467  346    1358   1348    1458    9    3567  3678

135   12356  7      159    1469    14569   12   8     349
18    1268   269    1789   146789  3       127  12479 5
4     1358   39     15789  2       1589    6    1379  379

(The swordfish in 4 doesnt really help)

Elminate 3 from r3c9:
r9c3=3,r7c9=3
. r8c3=9,r6c3=6,r3c3=4,r1c8=4,r7c9=4
=> r9c3=9

Eliminate 2 from r4c7:
r4c7=2,r7c7=1,r8c7=7,r9c8={39},r9c9={39}
not possible, because r9c3={39}
=> (2 numbers for 3 cells) r4c7=5

Eliminate 2 from r8c3:
r2c3=3->r1c1<>3
r3c3=4,(r1c2<>3),r1c2={78},(r1c7={78}),r1c1<>{78}
=> (no number left for r1c1) r8c3=6

Eliminate 2 from r4c8:
r4c8=2,r5c6=2,r4c4=2,r3c3=4
. r4c2=6,r4c5=4,r6c3=4,r3c3<>4
Eliminate 3 from r4c1:
r4c1=3,r6c3=4
. r4c8=6,r4c2=4.r6c3<>4
=>r4c1=9, r4c5<>9

Elminate 3 from r6c3:
r6c3=3,r4c2=4,(r4c5<>9),r4c5=3,r1c4=3
r2c3=2, r3c3=4 (r1c2<>4), triple {378} in row 1 (c127)->r1c4=9
=>r6c3=4

With this i got here:
Code: Select all
7   4   1     3   5    69     8  69  2
6   58  3     4   89   2      1  59  7
58  9   2     18  7    168    3  56  4

9   6   8     2   4    7      5  3   1
13  7   5     6   139  19     4  2   8
2   13  4     158 138  158    9  7   6

135 13  7     15  6    4      2  8   9
18  2   6     9   18   3      7  4   5
4   58  9     7   2    58     6  1   3

Matter of taste, eg
weak chain in 8: r2c2-r9c2~r9c6-r8c5~r2c5-r2c2 -> r2c2=8
or double forcing chain:
r8c1=1,r3c1=5,r2c2=8
r8c5=1,r2c5=9,r2c2=8
Wolfgang

Posts: 208
Joined: 22 June 2005