## Scientific American: Simple Groups at Play

Everything about Sudoku that doesn't fit in one of the other sections

### Scientific American: Simple Groups at Play

Read the article here, and play the puzzles here.

The puzzles are interesting and quite challenging. At the moment I'm working on M12. Any ideas for a general solution?
submacrolize

Posts: 12
Joined: 27 February 2008

Withdrawn.
Last edited by Luke on Tue Jun 24, 2008 10:21 am, edited 1 time in total.

Luke
2015 Supporter

Posts: 435
Joined: 06 August 2006
Location: Southern Northern California

You can view the solution here:
Code: Select all
`1 2 3 4 5 6 7 8 9 10 11 12`
eleven

Posts: 1948
Joined: 10 February 2008

An interesting puzzle which unfortunately will be overlooked because of the identity of the original poster. submacrolize I hope you have now realized that giving people the solutions alone means you will not get taken seriously and will refrain from chipping in with them continually.

Concerning the M12 puzzle. The repeated Merge/Invert operations so far posted on the Sciam page effectively act as a 'do nothing' operator. Merge 11 times does the same. No one has yet posted the transformations required to take a particular randomized sequence to the ordered sequence.
Glyn

Posts: 357
Joined: 26 April 2007

eleven wrote:You can view the solution here:
Code: Select all
`1 2 3 4 5 6 7 8 9 10 11 12`

Mauricio

Posts: 1174
Joined: 22 March 2006

This should work:
Its easy to place 1 and 2 to positions 1 and 2. Then
3 to pos 3: IMIM3IM2
4 to pos 4: M3IMIM3IM5 (from pos 8,9), IMIMIM2IMIM2IMIM (from pos 5, 12)
5 to pos 5: M3IM2IM5IM (from pos 7, 10, 12), MIM3IM2IM3IM5I (from pos 6, 11, 12)
If 4 or 5 are in other positions, use one move to bring it in position for the other.
eleven

Posts: 1948
Joined: 10 February 2008

You can find a workable program/algorithm in here:

http://www.hakank.org/minizinc/M12.mzn

The author, Hakan Kjellerstrand, also wrote heaps of programs for other well known puzzles/problems in his home page:

http://www.hakank.org/minizinc

This website has nothing to do with me, but I guess it's better than submacrolize's spamming of Sudoku solutions.
udosuk

Posts: 2698
Joined: 17 July 2005

Its not very helpful for me to see cryptic code in an exotic programming language. Can you explain, what it does ?
eleven

Posts: 1948
Joined: 10 February 2008

Excellent work eleven

This hopefully explains eleven's moves in more detail.

Its easy to place 1 and 2 to positions 1 and 2.
Merge until 1 is in Position 12 Then invert.
Merge until 2 is in Position 2.

3 to pos 3: leaving positions 1 and 2 unchanged
IMIM3IM2 takes position 3 through the cycle of positions {3,11,10,5,8,7,12,6,3}
(if 3 is in positions 4 or 9 it needs to be moved eg to position 8 using a move for position 4).
4 to pos 4: leaving positions 1,2 and 3 unchanged
M3IMIM3IM5 takes position 4 through the cycle of positions {4,9,8,4}
IMIMIM2IMIM2IMIM takes position 4 through the cycle of positions {4,12,5,4}
(if 4 is in positions 6,7,10,11 use moves for position 3 or 5 to move it first)
5 to pos 5: leaving positions 1,2,3 and 4 unchanged
M3IM2IM5IM takes position 5 through the cycle {5,10,12,7,5}
MIM3IM2IM3IM5I takes position 5 through the cycle {5,9,8,6,5}
(if 5 is in position 11 use a move for position 3 to shift it first)

Hope this is useful.
Glyn

Posts: 357
Joined: 26 April 2007

Thanks Glyn.

At the second glance one of the 3rd and 4th move is not needed. The cycles of the moves are:

Code: Select all
`1.IMIM3IM2 :         (1),(2),(3.6.12.7.8.5.10,11),(4,9)2.M3IMIM3IM5 :       (1),(2),(3),(4,8,9),(5,6,10),(7,11,12)3.IMIMIM2IMIM2IMIM : (1),(2),(3),(4,5,12),(6,7,8),(9,10,11)4.M3IM2IM5IM:        (1),(2),(3),(4),(5,7,12,10),(6,9,11,8)5.MIM3IM2IM3IM5I:    (1),(2),(3),(4),(5,6,12,11),(7,8,10,9)`

As Glyn pointed out, if the 3 is in position 4 or 9, you can use move 3 to bring it to pos 8 and (4 times) move 1 to pos 3.

Move 2 brings 4 to pos 4 from pos 9 or 8 (2 times).
If its not there, but in (5,6,10), first bring it to 6 (if necessary) by move 2, then to 9 by move 4 and to 4 by move 2 again.
If its in (7,11,12), bring it to 11 (move 2), then to 8 by move 4, then 2 times move 2 for pos 4.

Move 4 brings 5 to pos 5 from 7,12 and 10.
If its in (6,9,11,8), use move 4, until its in 6, then 3 times move 5 to pos 5.
eleven

Posts: 1948
Joined: 10 February 2008

eleven wrote:Its not very helpful for me to see cryptic code in an exotic programming language. Can you explain, what it does ?

I suppose it uses a brute-force approach to work out a solution to solve a M12 puzzle. For most of us it shouldn't be much helpful. But for submacrolize it should be as all he cares is the solution.

BTW nice scheme eleven. Let me guess - you're also a great Rubik's cube solver? Have you tackled the "Professor's Cube"?
udosuk

Posts: 2698
Joined: 17 July 2005

Is it just me who gets 403 errors trying the link?
wintder

Posts: 297
Joined: 24 April 2007

I think it must be just you having a problem with the link. Try approaching it from the Scientific American's main web page. Then select Magazine.

If you try the M24 puzzle note that you have to drag the numbers not enter L,R and S in Move History. The letters only work when assembling custom moves.

Matt I think that submacrolize has seen the error of his ways, but we will have to wait and see.

There are quite a few assemblies which achieve similar results. I guess the next task is to find the minimum set of I and M to achieve reordering. eg for moving the 3 (given 1 and 2 correct) we can use eleven's IMIM3IM2 or something else such as IM3IM6IM which reaches the parts the other one doesn't (but not all) and moves the 3 quicker from certain starting points.

Of course there is no reason to place 1 and 2 first anyway if a minimum set is required.
Glyn

Posts: 357
Joined: 26 April 2007

udosuk wrote:BTW nice scheme eleven. Let me guess - you're also a great Rubik's cube solver? Have you tackled the "Professor's Cube"?
Thanks.
I was crazy enough to bet, that i could do it in 3 days. When i thought, i finally got it on the 3rd day, i realized, that i needed a 3rd move for the corners (plus the one for the edges and one for the middle stones). So it became a long day too to repair it.
I did not bet again
eleven

Posts: 1948
Joined: 10 February 2008