## Two Trick Pony ?

Post puzzles for others to solve here.

### Two Trick Pony ?

Can you tame this beast in two moves ?

Code: Select all
`*-----------*|.2.|6..|..5||4..|..1|.3.||..9|...|...||---+---+---||8..|.23|.9.||...|4.6|...||.1.|78.|..2||---+---+---||...|...|1..||.7.|9..|..6||5..|..4|.8.|*-----------*`
Last edited by Leren on Mon Jun 25, 2018 6:32 am, edited 1 time in total.
Leren

Posts: 3343
Joined: 03 June 2012

### Re: Two Trick Pony

two move = 9r7c1+3r7c3

this puzzle can be solved by setting two digits .
Code: Select all
`  1  2  3  4  5  6  7  8  9  digit 20 24 33 24 31 24 33 24 20  no. of candidates(incl. clues)`

by setting 2 digits of each 3,5,7 (no. of candidates over 30)
for instance, 3r7c3+3r8c6 or 5r3c6+5r4c7 or 7r3c+7r4c9 etc.

i prefer N=9's symmetrical form as diagonal r1c1-r9c9.

Code: Select all
`|         |         |  9      ||         |     9   |         ||        9|         |         ||         |         |     9   ||     9   |         |         ||         |        9|         ||  9      |         |         ||         |  9      |         ||         |         |        9|`

regards
Last edited by Kozo Kataya on Thu Jun 21, 2018 4:28 am, edited 2 times in total.
Kozo Kataya

Posts: 33
Joined: 06 July 2012

### Re: Two Trick Pony

For me it is one move. Fill the diagonals with the possible digits.
eleven

Posts: 1976
Joined: 10 February 2008

### Re: Two Trick Pony ?

eleven wrote : For me it is one move.

I wasn't quite sure whether Main and Anti Diagonal symmetry counted as one move or two myself, so I've added a question mark to the thread title. I think it's a matter of semantics. BTW, Can you see the equally obvious symmetry in this one ?

Code: Select all
`*-----------*|..6|8..|..3||9..|.1.|.5.||...|..7|...||---+---+---||8.9|...|...||.13|2..|..7||42.|.6.|.1.||---+---+---||..8|5..|..2||...|...|6..||7..|.4.|.9.|*-----------*`

Leren
Leren

Posts: 3343
Joined: 03 June 2012

### Re: Two Trick Pony ?

Leren wrote:BTW, Can you see the equally obvious symmetry in this one ?

Code: Select all
`*-----------*|..6|8..|..3||9..|.1.|.5.||...|..7|...||---+---+---||8.9|...|...||.13|2..|..7||42.|.6.|.1.||---+---+---||..8|5..|..2||...|...|6..||7..|.4.|.9.|*-----------*`

Leren

It's not hard, if you know, that there are diagonal symmetries (but you should have an editor, which allows to copy/paste rectangle text for the column swaps).
First of all, box 4 must be the center, so you exchange stacks 1 and 2:
Code: Select all
`8.. ..6 ..3.1. 9.. .5...7 ... ...        ... 8.9 ...2.. .13 ..7.6. 42. .1.        5.. ..8 ..2... ... 6...4. 7.. .9.`

Then you know, that (from the main diagonal) 178 must correspond to 269 (boxes 19), 69 to 17 (boxes 26), and 26 to 78 (boxes 48)
The last 2 give the only possible mappings (67), (19), (28), and the other three (345) must map to themselves.
So 345 in boxes 357 must be in the diagonal, to achieve that, you can exchange rows 45 and 78, and columns 12:
Code: Select all
`.8. ..6 ..31.. 9.. .5...7 ... ...        .2. .13 ..7... 8.9 ...6.. 42. .1.        ... ... 6...5. ..8 ..24.. 7.. .9`
.
This already gives the double symmetry.
You can fill now the diagonals and transform it back by applying the swaps in the reverse order.
eleven

Posts: 1976
Joined: 10 February 2008

### Re: Two Trick Pony ?

Hi eleven, well I didn't follow all of that but I'm amazed at your symmetry spotting skills. Of course the puzzle is a morph of the Two Trick Pony so must have the double diagonal symmetry, although in a morphed form.

I wrote the appropriate code as a private joke and never thought that a human could "unmorph" the puzzle to reveal the underlying symmetry - nice to be proven wrong.

Cheers, Leren
Leren

Posts: 3343
Joined: 03 June 2012

### Re: Two Trick Pony ?

I had to learn that, when i "translated" Red Ed's groups to solver views.
And i remember that i enjoyed that learning (though it probably would have been more effective to write a program).
eleven

Posts: 1976
Joined: 10 February 2008

### Re: Two Trick Pony ?

Hi eleven.

One thing i don't understand is why you were able to spot that Box 2 had to be on the diagonal. The reason is that my morphing process is random, so Columns 1 and 2 in each stack could well have been swapped, with no box having an obvious diagonal symmetry. How would you have proceeded then ?

Leren
Leren

Posts: 3343
Joined: 03 June 2012

### Re: Two Trick Pony ?

Because box 4 is the only one with 6 givens, it had to go to the center for a double diagonal symmetry. The easy move was to switch stacks 1 and 2.
You could also rotate the stacks, bringing box 2 to box 3, to get an equivalent symmetry.
eleven

Posts: 1976
Joined: 10 February 2008