Hi Gfroyle and Ravel.

Gfroyle wrote:How is this one for difficulty?

This is a very nice puzzle, not only because I find it beautifully simmetric, but also because of the logic that can be used to solve it. Gfroyle, did you generate it yourself?

Ravel wrote:Looks as hard as some monsters here.

However, I certainly do not agree with this statement because the puzzle can be easily solved with some simple nice loops, contrary to the Norwegian monsters around here.

Ravel wrote:I can solve it with one step, showing that r5c2<>5, but need a monster chain with multiple inferences.

Very good. Just one question: how did you find that chain, and why did you considered the cell r5c2?

Ravel wrote:Lets see, with what the experts come up for this.

As far as I am concern, I did't try yet to solve the puzzle in one step, but in the meantime I found the following simple steps:

- Code: Select all
` *-----------------------------------------------------------------------------*`

| 9 1345 7 | 6 13458 3458 | 2 138 148 |

| 1345 8 134 | 2 1345 7 | 134 9 6 |

| 6 134 2 | 138 13489 3489 | 5 138 7 |

|-------------------------+-------------------------+-------------------------|

| 123458 7 13489 | 358 6 3458 | 1389 12358 12589 |

| 23458 2345 348 | 9 34578 1 | 378 6 258 |

| 1358 6 1389 | 3578 2 358 | 13789 4 1589 |

|-------------------------+-------------------------+-------------------------|

| 12478 124 5 | 178 1789 289 | 6 128 3 |

| 1238 9 138 | 4 1358 6 | 18 7 1258 |

| 12378 123 6 | 13578 13578 2358 | 49 1258 49 |

*-----------------------------------------------------------------------------*

1. [r2c1]=5=[r2c5]-5-[r8c5]=5=[r8c9]=2=[r8c1]-2-[r7c2|r9c2]=2=[r5c2]=5=[r1c2]-5-[r2c1],

which implies: r1c5,r5c5,r9c5<>5; r8c9<>1,8; r7c1,r9c1<>2; r5c2<>3,4.

2. [r4c1]-2-[r8c1]=2=[r8c9]-2-[r5c9]=2=[r5c1|r5c2]-2-[r4c1], => r4c1<>2.

3. [r5c9]-5-[r5c2]=5=[r1c2]-5-[r2c1]=5=[r2c5]-5-[r8c5]=5=[r8c9]-5-[r5c9], => r5c9<>5.

4. [r7c5]-1-[r1c5]=1=[r1c2]=5=[r5c2]=2=[r5c1]-2-[r8c1]=2=[r8c9]=5=[r9c8]=1=[r7c8]-1-[r7c5], => r7c5<>1.

5. [r7c6]=2=[r7c8]=1=[r9c8]-1-[r9c5]=(Almost Unique Rectangle: r7c1/r9c1/r7c5/r9c5)=1|9=[r7c5]-9-[r7c6],

which implies r7c6<>9 and that solve the puzzle.

Regards, Carcul