creint wrote:Solves nicely with diagonal symmetry from upper left to lower right:

Nice.

In the first step you can clear all but 159 from the diagonal. Then it is really simple.

[Added for completeness:]

Rotational symmetry maps the cells row n/colum m to row (10-n)/col (10-m), e.g. 7r2c4<->8r8c6. In the puzzle you can find only the digit mappings (1,5)(2,4)(3,6)(7,8). So it has the symmetry, and - if the puzzle is unique - the solution must have it too => the center r5c5 must be 9.

The symmetry at the main diagonal maps row n/col m to row m/col n, e.g 7r2c4<->3r4c2. Digit mappings here are (1,1)(2,4)(3,7)(5,5)(6,8). So you only can have 159 in the main diagonal of the solution.

The symmetry at the other diagonal maps row n/colum m to row (10-m)/col (10-n), e.g. 7r2c4<->6r6c8. Digit mappings here (1,5)(2,2)(3,8)(4,4)(6,7). So you only can have 249 in this sub diagonal.

[edit 2]:

Ooops, i had mixed E anf F transformation before. As blue (re)posted today, the E transformation can be defined as

"swapping rows 2&4, 3&7, 6&8, and columns 2&4, 3&7, 6&8".

So the original puzzle

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

| 1 . . | . . 6 | . 8 . |

| . . . | 7 . . | . . 3 |

| . . . | . 2 . | . . . |

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

| . 3 . | . . . | . . 7 |

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

| 8 . . | . . . | . 6 . |

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

| . . . | . 4 . | . . . |

| 6 . . | . . 8 | . . . |

| . 7 . | 3 . . | . . 5 |

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

goes to

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

| 1 . . | . . 8 | . 6 . |

| . . . | 3 . . | . . 7 |

| . . . | . 4 . | . . . |

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

| . 7 . | . . . | . . 3 |

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

| 6 . . | . . . | . 8 . |

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

| . . . | . 2 . | . . . |

| 8 . . | . . 6 | . . . |

| . 3 . | 7 . . | . . 5 |

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

and we have the number mapping (1)(24)(37)(5)(68)(9)

Since the transformation has the "fixed" cells r159c159 we can clear all but candidates 159 there.