eleven wrote:It is really annoying, that both of you did not mention, that you did need my first step in your solution paths.

So we looked for something, which was not there - how could we know, that you have a strange feeling, what is as easy as an xy-wing ? Otherwise it would have been very easy to find the second step.

(btw not to place a single at the beginning is just stupid for me.)

I guess the main point is not whether your logic is as easy as xy-wing, but how you present your move. The way you presented your move was by chains, and I specifically stated that the puzzle doesn't need chains to be solved. If you had used something other than chains to present your logic, then we could have the argument whether it's as easy as xy-wing.

Note my first two steps are as simple as "locked candidates" once you factor out the symmetrical element of the logic. I think roughly speaking there are 3 level of difficulties among techniques:

1. basic techniques:

singles, subsets, locked candidates (aka box-line intersection)

2. intermediate techniques:

simple fish (e.g. x-wing), turbot fish, xy-wing, w-wing, empty rectangle, sue de coq, etc

(and if uniqueness is allowed: UR, BUG, BUG-lite, etc)

3. advanced techniques:

forcing chain (including xy-chain), ALS (including ALS-xz), forcing net etc

So my intention was that you should solve the puzzle using the first 2 levels of techniques only.

eleven wrote:As a revenge here is an unfair challenge for you:

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

| . 9 6 | . . 5 | . 1 . |

| . . . | 3 . . | . . . |

| 2 . . | . . 6 | 5 . 9 |

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

| . . 5 | . . . | 6 . . |

| 9 4 2 | . . . | 3 . . |

| . . 3 | . . . | 1 9 4 |

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

| . 2 . | . . 4 | . . 1 |

| 5 . . | 8 . 2 | 4 . 7 |

| . 8 4 | 7 . 1 | . 6 . |

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

Nothing harder than xy-wing needed (no xy-chain).

Nice puzzle! I have a rough idea how to crack it using the least amount of work, but I can't straighten out my logic (yet). Here is a sketch of what I see:

First swap r45, then swap r78, then swap c56, then swap c89:

- Code: Select all
`+----------------------------+----------------------------+----------------------------+`

| 3478 9 6 | 24 5 2478 | 278 238 1 |

| 1478 157 178 | 3 789 124789 | 278 268 2478 |

| 2 137 178 | 14 6 1478 | 5 9 3478 |

+----------------------------+----------------------------+----------------------------+

| 9 4 2 | 156 78 15678 | 3 58 578 |

| 178 17 5 | 1249 3789 1234789 | 6 28 278 |

| 678 67 3 | 256 78 25678 | 1 4 9 |

+----------------------------+----------------------------+----------------------------+

| 5 136 19 | 8 2 369 | 4 7 3 |

| 367 2 79 | 569 4 3569 | 89 1 358 |

| 3 8 4 | 7 1 359 | 29 235 6 |

+----------------------------+----------------------------+----------------------------+

Note despite b258 being a mess we have perfect 180 degree rotational symmetry @ b13, b46 & b79 respectively with the digit mapping 1-2, 5-6, 7-8 and 3-3, 4-4, 9-9. If we can somehow prove that this symmetry must be conserved in the solution then this puzzle can be solved in one simple move - r8c37=[78]. (Remember to swap back the rows/columns to produce the solution for the original puzzle.)

(I suppose one might use a uniqueness line of argument as follows: say r8c37=[79] yields a solution, then you can argue that r8c37=[98] must produce another solution using the rotational operations on b13, b46, b79 with digit remapping.)

RW, what duya think?