## pentomino/sudoku cross

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

### pentomino/sudoku cross

I've made a puzzle from the set of 12 pentominoes, plus the square
tetromino. The shapes are labelled with one of the numbers 1-8 on each
square. You have to try and fit them into an 8x8 square so that each
row and each column contains the numbers 1-8. You'll find it here:
http://uk.geocities.com/aidan_001/puzzles2.html
There are over 16000 ways of putting the shapes into the 8x8 square,
but I don't know how many of them will also solve my puzzle (at least
one will). Also as several of the shapes have symmetries, by putting
numbers on them you can multiply this total by some power of 2 . It'd
be nice to create a version of this that has a unique solution.
ab

Posts: 451
Joined: 06 September 2005

When you say "each piece can be turned over", do you mean that we can imagine it to be a clear piece of plastic and flip it so that the upper side becomes the bottom side?

Or are we to imagine them to be like dominos, with the pattern on only one side?

Looks nice though..

Gordon
gfroyle

Posts: 214
Joined: 21 June 2005

I meant you could turn over the piece as though it were made of clear plastic, or in other words marked the same way on both sides, except a mirror image.

Glad you like the look of it. Have fun solving it.
ab

Posts: 451
Joined: 06 September 2005

### Pentomino Sudoku Has No Solution

This particular puzzle has no solution

If you make a frequency count of the dots on each of the 64 squares,
you find that dot count "1" is nine and dot count "6" is seven.

Each dot count must be eight.
holdout

Posts: 35
Joined: 30 August 2005
Location: Bowie, Maryland USA

Thanks for pointing that out. That was careless of me. I had also made another mistake. However I have loaded up a new image which I'm sure is correct. So feel free to have another go
http://uk.geocities.com/aidan_001/puzzles2.html
Hve fun
ab

Posts: 451
Joined: 06 September 2005

Aside from reflections and/or orientation differences, the only solution is:

Code: Select all
`**********************************   *   *           *           ** 2 * 6 * 5   1   7 * 4   8   3 **   *   *           *           **   *   *       *********   ******   *   *       *       *   *   ** 4 * 8 * 6   3 * 1   2 * 5 * 7 **   *   *       *       *   *   **   *   *********       *   *   **   *       *   *       *   *   ** 8 * 3   7 * 4 * 6   5 * 2 * 1 **   *       *   *       *   *   **   *   *****   *************   **   *   *       *   *           ** 6 * 4 * 1   2 * 8 * 3   7   5 **   *   *       *   *           **   *****   *****   **************   *       *   *           *   ** 5 * 7   2 * 6 * 4   1   3 * 8 **   *       *   *           *   **************   *********   *   **       *   *           *   *   ** 1   5 * 3 * 8   2   7 * 6 * 4 **       *   *           *   *   **   *****   *****   *********   **   *           *   *       *   ** 3 * 1   8   7 * 5 * 6   4 * 2 **   *           *   *       *   **   *****   *********   *****   **       *   *           *       ** 7   2 * 4 * 5   3   8 * 1   6 **       *   *           *       **********************************`
holdout

Posts: 35
Joined: 30 August 2005
Location: Bowie, Maryland USA

holdout wrote:Aside from reflections and/or orientation differences, the only solution is:

As you're claiming it's the only solution, did you use a program to solve it?
If there is only one solution that was simply a fluke on my part
ab

Posts: 451
Joined: 06 September 2005

To: ab

Yes, I wrote an ad-hoc C-program for solution.

My guess is that for an 8 x 8 jigsaw puzzle of this type (13 pieces of different shapes) you will normally have only one answer.

There were a total of 8 solutions, including the one published.
holdout

Posts: 35
Joined: 30 August 2005
Location: Bowie, Maryland USA

thanks for that, holdout.

It begs the question.. do you think problems like this are harder than normal pentomino problems, or do the numbers really aid the search?

I mean without the numbers there are 16000+ solutions to that problem, which when you add in rotations and reflections becomes 128000. But adding the numbers means that only 8 of these 128000 solve the problem.

Also I'll have to find a problem with more than one solution
ab

Posts: 451
Joined: 06 September 2005

To: ab

Since I was more interested in writing a program, I really didn't spend any time doing it by hand.

I suppose the easiest way would have been to cut-out the pieces and put them together just like a jig-saw puzzle. The permutation restrictions are very strong. It would have taken less time, I believe.
holdout

Posts: 35
Joined: 30 August 2005
Location: Bowie, Maryland USA

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