## Help with a puzzle

For fans of all other kinds of logic puzzles

### Help with a puzzle

Hi! I have been trying to solve this puzzle for some time now and I just can't get it. It is not a Sudoku, but similar so I hope it is ok to post here.
Puzzle - Around each red number are 8 white squares, and each white square should have a number from 1 to 7. Once filled in, these 8 numbers will sum to the red number. In addition, once completed correctly, no row nor column will contain a duplicate number within a white square.
Thanks in advance for any help you can give me. It is driving me crazy, and I really want to see the solution. Cheers.
puzzle
c00cfe74-4141-4874-ba37-f8c886e7d353_l.jpg (34.62 KiB) Viewed 1135 times
geocacher

Posts: 2
Joined: 14 April 2017

### Re: Help with a puzzle

Hmm, interesting. By "no row nor column will contain a duplicate number within a white square", I assume you mean that each row or column consisting of 7 white cells will contain each number 1-7 exactly once, and that each row or column consisting of 4 white cells will contain each number 1-7 at most once.

Looks difficult. Maybe I'll give it a try in the next day or two.

Or maybe there are multiple solutions, in which case whoever thought it up gets a raspberry.

Bill Smythe
Smythe Dakota

Posts: 564
Joined: 11 February 2006

### Re: Help with a puzzle

Here is the unique solution :

Code: Select all
| 4   3   7   1   6   2   5 |
| 5  35   3  26   1  29   4 |
| 7   5   1   4   3   6   2 |
| 2  34   6  29   4  35   7 |
| 3   6   4   2   5   7   1 |
| 1  28   5  32   2  35   6 |
| 6   1   2   5   7   4   3 |

Leren
Leren

Posts: 4008
Joined: 03 June 2012

### Re: Help with a puzzle

Awesome. You are amazing. I have spent countless hours on it without success, but is looks like I was close. So happy to see it solved. Thanks.
geocacher

Posts: 2
Joined: 14 April 2017

### Re: Help with a puzzle

I'm glad to hear it has only one solution. There are plenty of garbage websites out there featuring (Sudoku and other) puzzles with multiple solutions. And the people who created those don't even seem to think it matters.

Bill Smythe
Smythe Dakota

Posts: 564
Joined: 11 February 2006

### Re: Help with a puzzle

Just when you thought you were safe, and geocatcher's puzzle had been solved, here is another one of the same type.

Code: Select all
|  1   2   5   3   6   7   4 |
|  x  29   x  37   x  31   x |
|  x   x   x   x   x   x   x |
|  x  30   x  30   x  31   x |
|  x   x   x   x   x   x   x |
|  x  33   x  31   x  30   x |
|  2   7   6   1   4   3   5 |

The solution is unique.

Leren
Leren

Posts: 4008
Joined: 03 June 2012

### Re: Help with a puzzle

Found another reference to this type of puzzle here.

Although there are no clues other than the summation numbers, there are 1,564 solutions, so finding at least one of them should be a doddle.

Leren
Leren

Posts: 4008
Joined: 03 June 2012

### Re: Help with a puzzle

Leren wrote:Found another reference to this type of puzzle here .... [where] there are 1,564 solutions, so finding at least one of them should be a doddle. ....

Solving a puzzle with multiple solutions is no doddle, if you start with the (reasonable) assumption that the solution is unique. You'll quickly (maybe even immediately) run into a situation where there is no logic to direct you to the next fill-in. It is very bad form to present a puzzle with multiple solutions, unless the poster states that the puzzle has multiple solutions, and also states what the solver's objective should be -- e.g. to find (or at least count) all solutions, or to find just one solution (but that's tacky and trivial), or simply to find out whether the solution is unique, or whatever.

Bill Smythe
Smythe Dakota

Posts: 564
Joined: 11 February 2006

### Re: Help with a puzzle

I wasn't being serious when I said that finding at least one solution to the 40 blank cell problem was a doddle.

In fact the problem appears to be of Exponential complexity, which is to say that to find a solution to this sort of puzzle with N blank cells requires O(7^N) operations.

This would be completely intractable, even for a computer, without the constraints given in the first post. Fortunately the constraints reduce the problem to a manageable one.

If it makes you feel better, here is an example from the Brainbashers puzzle, with the first and last rows filled in. The solution is unique.

Code: Select all
|  2   4   3   7   6   5   1 |
|  x  26   x  35   x  37   x |
|  x   x   x   x   x   x   x |
|  x  31   x  36   x  39   x |
|  x   x   x   x   x   x   x |
|  x  38   x  26   x  24   x |
|  7   6   4   2   3   1   5 |

Leren
Leren

Posts: 4008
Joined: 03 June 2012

### Re: Help with a puzzle

Loren,

Lest anybody think I was criticizing you, let me set the record straight. In fact, you did us all a favor by pointing out the bogosity of the Brainbashers puzzle.

Brainbashers, however, earns a raspberry.

Bill Smythe
Smythe Dakota

Posts: 564
Joined: 11 February 2006