Logic Games Tatami

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disoriented
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Logic Games Tatami (+1)

So this is a Tatami puzzle from the iOS (and Windows Phone) app Logic Games.

The objective is to fill each space with a number from 1 to 6 such that:
- each six-space box contains every number once
- each row contains every number twice
- each column contains every number twice
- no two horizontally or vertically adjacent spaces contain the same number

This one has me stumped. How do you solve it?

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[Last edited by disoriented at 11-15-2014 08:47 PM]

11-12-2014 at 11:33 PM

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TripleM
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Re: Logic Games Tatami (+1)

Have you filled in any of the grid, or are you yet to get started?

My first steps would be:

Click here to view the secret text

11-13-2014 at 12:16 AM

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disoriented
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Re: Logic Games Tatami (0)

I've filled in a bit, but haven't solved it. i wanted to present the puzzle as I first saw it, to see if the smart people on this forum could get the solution.

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[Last edited by disoriented at 11-13-2014 07:33 AM]

11-13-2014 at 07:32 AM

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TripleM
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Re: Logic Games Tatami (+2)

Whew, that was tough. Managed to fill in the majority of the grid but got stuck near the end and couldn't see any way of progressing. In the end I had to concede and choose one of two options and see which way worked.

Click here to view the secret text

1 5 6 2 4 3|4 6 2 5 1 3
-----------------------
6 1 2 4 3 5|1 2 3 6 5 4
-----------------------
1|6|1 2 6 4 3 5|2|4|3|5
 | |-----------| | | |
6|5|6 4 5 3 1 2|1|2|4|3
 | |-----------| | | |
2|1|5 1 2 4 6 3|4|3|5|6
 | |-----------| | | |
4|2|4 3 1 6 2 5|3|5|6|1
 | |-----------| | | |
3|4|3 5 2 1 6 4|5|6|1|2
 | |-----------| | | |
5|3|5 6 3 2 4 1|6|1|2|4
-----------------------
2 6 3 1 4 5|2 6 1 4 3 5
-----------------------
4 2 1 3 5 6|5 4 6 3 2 1
-----------------------
3 4 2 5 6 1|3 1 5 2 4 6
-----------------------
5 3 4 6 1 2|5 3 4 1 6 2

[Last edited by TripleM at 11-14-2014 10:40 PM]

11-14-2014 at 10:39 PM

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disoriented
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Re: Logic Games Tatami (0)

Nice job! Have a couple of mod points. If you enjoy this stuff, I'll post another puzzle.

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11-15-2014 at 04:17 AM

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disoriented
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File: example_neighbors.png (5.3 KB)
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Logic Games Neighbors (+1)

OK, here's a hard one for you.

Divide the grid into tetronimoes (Tetris pieces) along the gridlines. A number on a tetromino indicates how many neighbors that tetromino touches. Corners do not count as touching.

An example solved grid is below:

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[Last edited by disoriented at 11-15-2014 08:45 PM]

11-15-2014 at 08:39 PM

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disoriented
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File: neighbors.png (4.7 KB)
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Re: Logic Games Neighbors (+1)

Now the puzzle:

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[Last edited by disoriented at 11-15-2014 08:44 PM]

11-15-2014 at 08:41 PM

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TripleM
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File: tetromino.png (19.2 KB)
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Re: Logic Games Tatami (+1)

OK, I have no idea how to figure this out with any logical method.

But I managed to write a solver:

12-27-2014 at 01:05 AM

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disoriented
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Re: Logic Games Neighbors (0)

Very good!

My solver never found a solution for this size grid in reasonable time. I was doing straightforward backtracking: placing a tetromino, then recursively searching the remainder of the grid, backing up when an impossible situation was detected. This works well on up to 6x6 but not so much beyond that.
EDIT: From your comment below, it seems like my search pattern does a lot of repetitive work.

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[Last edited by disoriented at 12-27-2014 07:14 AM]

12-27-2014 at 04:02 AM

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TripleM
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Re: Logic Games Tatami (0)

I just did backtracking, though always considering the squares from top left to bottom right, looping over all tetrominoes that cover the next empty square and exactly one number. After each one is placed, I run a check that:

known neighbours <= tetromino's value <= known neighbours + number of adjacent empty squares

for all placed tetrominoes so far, and return early if that doesn't hold.

Running time 0.4s.

12-27-2014 at 04:18 AM

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