June 19 Nightmare

[AZ Matt]

June 19 Nightmare: Wow... I am stuck here:

Code: Select all

346  2346  8     1234  7    5     136  9    1234
9    5     24    6     128  234   1378 1478 123478
1    7     246   2348  9    234   3568 2458 2348

457  1249  1247  2459  3    8     1247 1247 6
78   24    3     24    6    1    9     78   5
4568 12469 1246  7     25   249   18   3    1248

2    8     167   135   4    367   1357 157  9
367  136   9     12358 1258 2367  4    1578 1378
347  134   5     1389  18   379   2    6    1378

I've tried colouring, forcing chains -- what am I missing?

I bet it is obvious...

[Ruud]

You are missing, not necessarily in this order:

4 Line-box interactions
1 Naked pair
2 Hidden pairs
1 X-Wing
1 XY-Wing
1 XYZ-Wing
2 Finned X-Wings
1 Finned Swordfish
2 Nishio steps



But maybe there are quicker ways to solve this puzzle. Some of our regular guests may be able to help you.

Welcome to the site and forum!

Ruud.

[GreenLantern]

From your starting grid, the following basic steps can be applied:

• Removing 24 from r4c7
• Naked Triple (178) in Box 6 => r4c8<>17, r6c9<>18
• Locked Candidate '3' in Box 1 => r1c479<>3
• Locked Candidate '1' in Box 6 => r127c7<>1
• Hidden Single '6' in Box 1 => r3c3=6
• Hidden Single '6' in Row 7 => r7c6=6

Code: Select all

+-------------------------+-------------------------+-------------------------+
| 34      234     8       | 124     7       5       | 6       9       124     | 
| 9       5       24      | 6       128     234     | 378     1478    123478  | 
| 1       7       6       | 2348    9       234     | 358     2458    2348    | 
+-------------------------+-------------------------+-------------------------+
| 457     1249    1247    | 2459    3       8       | 17      24      6       | 
| 78      24      3       | 24      6       1       | 9       78      5       | 
| 4568    12469   124     | 7       25      249     | 18      3       24      | 
+-------------------------+-------------------------+-------------------------+
| 2       8       17      | 135     4       6       | 357     157     9       | 
| 367     136     9       | 12358   1258    237     | 4       1578    1378    | 
| 347     134     5       | 1389    18      379     | 2       6       1378    | 
+-------------------------+-------------------------+-------------------------+

From here, I applied the following steps to solve the puzzle:

• Multicoloring in 7's: r47c3,r4c7,r5c8 => r7c8<>7
• [r1c2]=2=[r2c3]=4=[r46c3]-4-[r5c2]-2-[r1c2] => r46c12<>4, r46c2<>2
• [r4c2]=9=[r4c4]-9-[r6c6]=9|1=[r6c3]-1-[r4c2] => r4c2<>1
• [r8c4]=8=[r4c4]-8-[r2c5]=8|2=[r8c6]-2-[r8c4] => r8c4<>2
• Multicoloring in 8's: r38c4,r9c59 => r3c9<>8
• [r9c9]=8=[r9c5]-8-[r2c5]=8=[r3c4]=3=[r23c6]-3-[r9c6]-7-[r9c9] => r9c9<>7
• [r4c1](-7-[r5c1])=5=[r6c1]=6=[r6c2]=1=[r46c3]-1-[r7c3]-7-[r89c1]=7=[r4c1] => r6c1=56
• [r4c3]=7=[r7c3]=1=[r89c2]-1-[r6c2]-6-[r6c1]-5-[r4c1]=5=[r4c4]=4=[r5c4]-4-[r5c2]-2-[r4c3] => r4c3<>2
• [r2c9]=7=[r8c9]-7-[r7c7]=7=[r7c3]-7-[r4c3]-4-[r4c8]-2-[r6c9]-4-[r2c9] => r2c9<>4
• [r6c3]=4=[r6c9]-4-[r1c9]=4=[r1c12]-4-[r2c3]-2-[r6c3] => r6c3<>2
• Unique Rectangle (34): r19c12 => r8c1<>7, r8c2<>1
• Coloring in 2's: r3c68,r4c48,r6c59,r8c56 => r4c8/r6c5/r8c6=2

[AZ Matt]

I don't know how I got the 24 as candidates in r4c7. That was it. Thanks.