- Code: Select all
` |.3.|...|67.|`

|.1.|3..|..2|

|7.9|...|..3|

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

|...|.5.|...|

|.56|2..|...|

|...|1..|9.5|

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

|89.|.3.|.46|

|.41|..8|.5.|

|5..|..4|2.8|

I have been teached Sticks symmetry already twice:

here and

hereNow, yzfwsf has added it to his solver, and Leren had solved the puzzle within minutes. A manual solution is of little interest.

Nevertheless, here is my way to a manual solution.

In any symmetry, the candidates are symmetric, and so is the pattern.

First look at the pattern:

The number of givens in boxes maps as follows:

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` | 4 | 1 | 4 |`

| 2 | 3 | 2 |

| 5 | 3 | 5 |

The similarity between stacks 1, 3 is a clue for a row sticks symmetry, with sticks located in stack 2.

Let's try to find similar patterns in pair of boxes [13] and [79]. A permutation of columns is need in stack 3.

Swapping circularly columns 7,8,9 to [7->9, 8->7, 9->8].

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` |.3.|...|7.6| `

|.1.|3..|.2.|

|7.9|...|.3.|

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

|...|.5.|...|

|.56|2..|...|

|...|1..|.59|

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

|89.|.3.|46.|

|.41|..8|5..|

|5..|..4|.82|

At that point, it is easy to find the sticks: in b2, r2c456; in b5, r4c456, in b8, r7c456 (the rows that have a pattern different from the other two's). From there, the automorphism is obvious:

swap stacks [13], then swap rows [13] [56] [89] (the sticks don't move)

Edit: corrected the diagram below, as well as the followings, consistently with the above (thanks to Leren for spotting the mistake)

Correction: swapped rows [56] [78]

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` |.3.|...|7.9|`

|.2.|3..|.1.|

|7.6|...|.3.|

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

|...|.5.|...|

|.59|1..|...|

|...|2..|.56|

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

|46.|.3.|89.|

|.82|..4|5..|

|5..|..8|.41|

then carry out digit permutation [12] [48] [69] [3] [5] [7]. The above puzzle is recovered:

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` |.3.|...|7.6|`

|.1.|3..|.2.|

|7.9|...|.3.|

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

|...|.5.|...|

|.56|2..|...|

|...|1..|.59|

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

|89.|.3.|46.|

|.41|..8|5..|

|5..|..4|.82|

Back to the start puzzle by the inverse of the initial isomorphism: swapping circularly columns 7,8,9 to [7->8, 8->9, 9->7].

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` |.3.|...|67.|`

|.1.|3..|..2|

|7.9|...|..3|

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

|...|.5.|...|

|.56|2..|...|

|...|1..|9.5|

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

|89.|.3.|.46|

|.41|..8|.5.|

|5..|..4|2.8|

Note that the puzzle is rated SE 9.2

The way to use the symmetry has been given by Leren.