## Logikion, the new Sudoku?

A forum for good logic/math puzzles.

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ConMan
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### Logikion, the new Sudoku?

Probably not. But it's a variant on sudoku that does present some interesting breaks from the standard patterns. A link to its introduction, including the first ever puzzle: http://blogs.abc.net.au/nsw/2011/07/our-new-puzzle.html

I just solved it, but it was in breaks at work so I didn't time myself. It's ... different, and while some of the methods I use for sudoku work on it, I used a lot of "determine every possible placement of numbers in the row/column/cluster and hope there's an obvious single possibility somewhere".
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AvatarIII
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### Re: Logikion, the new Sudoku?

that was pretty fun, i used to do suduko all the time but got bored eventually, this is a nice twist,
i too did it in little bits so couldn't really time myself either

i put the solution onto an image. sorry about the handwriting, i am lefthanded but use mice right handed.
Spoiler:

TaylorP
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### Re: Logikion, the new Sudoku?

I agree, the puzzle was a pleasant twist on Sudoku. I particularly like the idea of breaking up one of the colored segments into multiple pieces. I feel that even on its own, this would be an interesting feature to add to Sudoku. Maybe take a way a few clue numbers, and instead had 9 colored squares that also need to include 1-9. I don't think this particular one is solvable as I simply grabbed an existing sudoku and filled some squares, but something like this:
sudoku.jpg (70.71 KiB) Viewed 6734 times

Maybe this has been done before though? I'm not a hardcore puzzler.

AvatarIII
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### Re: Logikion, the new Sudoku?

TaylorP wrote:I agree, the puzzle was a pleasant twist on Sudoku. I particularly like the idea of breaking up one of the colored segments into multiple pieces. I feel that even on its own, this would be an interesting feature to add to Sudoku. Maybe take a way a few clue numbers, and instead had 9 colored squares that also need to include 1-9. I don't think this particular one is solvable as I simply grabbed an existing sudoku and filled some squares, but something like this:
sudoku.jpg

Maybe this has been done before though? I'm not a hardcore puzzler.

i'm pretty sure most sudoku's only have one answer, so randomly filling in squares is not going to give a solvable puzzle, but i also feel that doing what you suggest without taking away a few starter numbers is just going to make the puzzle easier, because there's a whole new block of 9 you know can't have double numbers in.

i decided to have a go at designing a logikion so i took this, a solved suduko puzzle, it's a bit rought but i just did it quickly in paint. if you want to try, the finished product is in the final spoiler tag, all the other tags give away the solution.
Spoiler:

then did this to isolate the numbers
Spoiler:

then chose areas each area having one of each number
Spoiler:

(the 9 and 8 to the lower left corner were supposed to be lavender, oops)

then i just wiped out a bunch of numbers leaving about 4 or 5 in each row and sector, i could probably wipe more but i didn't want it to be too hard.
Spoiler:

Aro
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### Re: Logikion, the new Sudoku?

The problem in your construction is that, because you didn't rearrange the numbers, you can solve it as a regular sudoku. It is just a regular sudoku but simpler to solve because you gave more rules (clues...).

I think it is far more difficult to construct a real logikion and that it is unlikely you can obtain one starting from a regular sudoku...

AvatarIII
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### Re: Logikion, the new Sudoku?

Aro wrote:The problem in your construction is that, because you didn't rearrange the numbers, you can solve it as a regular sudoku. It is just a regular sudoku but simpler to solve because you gave more rules (clues...).

I think it is far more difficult to construct a real logikion and that it is unlikely you can obtain one starting from a regular sudoku...

this is true, but if you were not to tell the solver that it is constructed from a normal sudoku, they would not know until it was solved, and so without that knowledge, they could not use it to help solve the puzzle.

Aro
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### Re: Logikion, the new Sudoku?

This is true but... it's not perfect ! I don't like imperfection. bleah.

AvatarIII
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### Re: Logikion, the new Sudoku?

Aro wrote:This is true but... it's not perfect ! I don't like imperfection. bleah.

if anything it's even more perfect, if you were to say that it works like a logikion and regular sudoku, you could get rid of more numbers probably, and it would be quite a hard puzzle

Sruixan
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### Re: Logikion, the new Sudoku?

It turns out that making one of these up completely from scratch is somewhat tantamount to going at your brain with a shotgun. I decided to work with a 7x7 grid just to make life a bit easier and as it happened I'm rather glad I did; it took about five minutes to put on some pretty patterns and stick seven random numbers in, then it took about two hours to move them about a bit so that there was an actual solution. Heck, I don't even know if it's a unique solution or not, but still, it's doable and that's good enough for me...

All rows, columns and coloured areas (red, blue, navy, green & purple) must contain the numbers 1 to 7.

I'd like to call this a Septoku but I expect I would get shot for it.
This is, er, no offense but you are a robot, aren't you?
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AvatarIII
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### Re: Logikion, the new Sudoku?

Sruixan wrote:It turns out that making one of these up completely from scratch is somewhat tantamount to going at your brain with a shotgun. I decided to work with a 7x7 grid just to make life a bit easier and as it happened I'm rather glad I did; it took about five minutes to put on some pretty patterns and stick seven random numbers in, then it took about two hours to move them about a bit so that there was an actual solution. Heck, I don't even know if it's a unique solution or not, but still, it's doable and that's good enough for me...

All rows, columns and coloured areas (red, blue, navy, green & purple) must contain the numbers 1 to 7.

I'd like to call this a Septoku but I expect I would get shot for it.

what about the brown areas? you have 14 brown squares, why didnt you turn them into sectors? they must have the numbers 1-7 in them twice, so why not?

Sruixan
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### Re: Logikion, the new Sudoku?

I didn't find it necessary to have them split (I daresay you can deduce how they are partitioned without too much difficulty, but you don't need that information to solve the grid) but if you want completeness, then all the brown squares above the green line are together and all the ones below are the final section. I'm guessing that info makes it a bit easier...
This is, er, no offense but you are a robot, aren't you?
That's just, um, beautiful, beautiful beautiful... just beautiful.
One hot summer's night Lorraine said: "It's time for you to see the lighthouse"
Dr. Ivanovich, was it really necessary?

lightvector
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### Re: Logikion, the new Sudoku?

This one doesn't have any disconnected regions, but I think it's a nice 5x5. Can you solve it without guessing?

squigglysudoku.png (3.89 KiB) Viewed 6504 times

Edit: I've never seen disconnected regions before, actually. But just for non-box-shaped regions, I think this type of puzzle has been around for a while, as "jigsaw sudoku", or "wiggly sudoku", or "squiggly sudoku". Here's a 7x7 that I designed by hand a while ago, which should be nice and pleasant to solve if you find the first few opening tricks. Although there might be other good ways to open it up.

Edit: Fixed error drawing two of the regions in second puzzle.

squigglysudoku2.png (4.27 KiB) Viewed 6422 times
Last edited by lightvector on Sat Jul 30, 2011 4:14 pm UTC, edited 1 time in total.

TaylorP
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### Re: Logikion, the new Sudoku?

I like your second puzzle, lightvector. I'm in the middle of solving it now, but I thought I'd post my colored version in case anyone else wants it. I found that on my monitor it was a bit easier to see the sections that way.

squigglysudoku2.png (7.21 KiB) Viewed 6498 times

Sruixan
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### Re: Logikion, the new Sudoku?

lightvector, your first little problem is a neat little gem. I solved it using the same method as I used to check my own invented grid for solutions and not only did it work beautifully it also didn't have too nasty a cascade at the end, whereby all the remaining numbers fall into place without thought. 15 minutes well spent. I shall have to try your other one tomorrow...

Spoiler:
5 4 2 3 1
1 2 3 5 4
3 5 1 4 2
2 3 4 1 5
4 1 5 2 3
This is, er, no offense but you are a robot, aren't you?
That's just, um, beautiful, beautiful beautiful... just beautiful.
One hot summer's night Lorraine said: "It's time for you to see the lighthouse"
Dr. Ivanovich, was it really necessary?

Sandor
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### Re: Logikion, the new Sudoku?

lightvector wrote:Here's a 7x7 that I designed by hand a while ago, which should be nice and pleasant to solve if you find the first few opening tricks. Although there might be other good ways to open it up.

Your 7x7 puzzle has one area of 6 squares, and one of 8. Is that how it's supposed to be?

squigglysudoku2_isthiscorrect.png (10.26 KiB) Viewed 6431 times

lightvector
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### Re: Logikion, the new Sudoku?

Ack, sorry, I misplaced one of the lines when drawing it into the computer. Fixed!

ConMan
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### Re: Logikion, the new Sudoku?

pollywog wrote:
Wikihow wrote:* Smile a lot! Give a gay girl a knowing "Hey, I'm a lesbian too!" smile.
I want to learn this smile, perfect it, and then go around smiling at lesbians and freaking them out.

WarDaft
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### Re: Logikion, the new Sudoku?

It seems like the most straight forward way to generate one of these is just to take a Latin Square and colour it randomly, then rearrange it and try to make it look nicer. Or don't rearrange, and really drive people mad.

Hmm, I see a generalization to an arbitrary number of 'virtual' dimensions here. Squares could be associated with colour groups, shape groups... when we run out of ideas, we can even just group them numerically. We might have a solvable 50 by 50 puzzle with only a handful of numbers actually on it.
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TheDancingFox
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### Re: Logikion, the new Sudoku?

I've seen these before labeled as a different variety of Sudoku. There are a lot of fun twists when you start really looking around.

Hehe, if we're talking about adding arbitrary virtual dimensions, why not also consider adding a physical dimension? 9 x 9 x 9 grid! Now that's a difficult puzzle. Also, impossible to properly observe with reasonable capability to understand which groups are which. I mean, it's possible...I've got 3d Minesweeper and it works great. I'm really curious about making a 3d Sudoku puzzle now. There would need to be lots of hints, and you would need to be able to look at every slice from any direction, probably. Would have to figure out where the groupings of 9 are. Is it every group of nine 3x3 sections of all 9 planes in all three directions? Now that would be a hard puzzle to design.

lightvector
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### Re: Logikion, the new Sudoku?

One interesting concept I've seen is a size 4 "sudokube". You have to place the hexadecimal digits 0 through F on the six faces of a cube where each face is a 4x4 grid. Each face has to contain exactly one of each digit, and each row/column followed all the way around the cube (as it wraps through 4 faces) must also contain exactly one of each digit.

I tried designing one by hand once. My sudoku solving skills were not good enough to stop me from trapping myself into an inconsistency when placing the numbers. But a good computer program could probably generate some.

tkxxx7
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### Re: Logikion, the new Sudoku?

a three-dimensional sudoku would be amazing.

The only twists I've found are those "high-5" or "samurai" sudokus, which are just five puzzles sharing 3x3 sections.

beany
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### Re: Logikion, the new Sudoku?

you guys are so insane....but so right insane......

i love sudoku....and this is great.... LOGIKION.....

im gonna play...cheers
beany