## Crossword Squares

Anything goes, but keep it seemly...

### Re: Crossword Squares

Yes I climbed the right mountain, just a minor bug in the drawing code - (the second time I've done that). I've corrected my diagram.

Congratulations to you for finding a second 160 solution.

I'm currently doing a survey to see if there are any other 160 solutions I can find. After that I think it's only fair that I propose the next pattern, if you are still up for it.

Leren
Leren

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Joined: 03 June 2012

### Re: Crossword Squares

OK. One more for the road!

JPF
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### Re: Crossword Squares

As I said in my previous post I said I'd do a survey to see if there were any more 160 solutions to the last pattern. Here is what I found.

JPF's 160 solution was one of a cluster of 8.

The solutions I initially found all had one thing in common, they all had the word CHECHAQUO in Column 3. Here are the results of a "vicinity" search using this word, checking many solutions with the values in Row 1 and Column 3 fixed, listed by the word that occupied Row 1.

BACKFLIPS...........267
JACKFRUIT............52
JACKPLANE...........86
JOCKEYING..........135
JOCKEYISM........1,577
JOCKSTRAP..........123

I decided to stop searching on each Row 1 word when when my solution counter hit it's maximum value of 2,147,483,647, so the results should be taken as minimums.

That's 2,248 160 solutions that I know about. So maximal solutions may be hard to find initially, but finding one may give you a clue to where many more are lurking.

Nevertheless they obviously form a tiny fraction of the total number of solutions, which is .... countless billions.

Leren
Last edited by Leren on Sat Jun 03, 2017 8:15 am, edited 9 times in total.
Leren

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Joined: 03 June 2012

### Re: Crossword Squares

Hi Leren,

Congratulaions for this study to the glory of scrabble-like-crossword squares science!
If you have a new pattern in mind it would be fair to start working on it both of us at the same time.
Picking a new pattern shouldn't take more than a minute.

JPF
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### Re: Crossword Squares

OK the pattern I have in mind is

Code: Select all
`---------------------| # Z Z Z Z Z Z Z # || Z Z Z Z Z Z Z Z Z || Z Z # Z Z Z # Z Z || Z Z Z Z Z Z Z Z Z || # Z Z Z # Z Z Z # || Z Z Z Z Z Z Z Z Z || Z Z # Z Z Z # Z Z || Z Z Z Z Z Z Z Z Z || Z Z Z Z # Z Z Z Z |---------------------`

For the avoidance of any doubt there are ten black squares at r1c1, r1c9, r3c3, r3c7, r5c1, r5c5, r5c9, r7c3, r7c7 and r9c5. Scrabble rules as per usual, top possible score 160.

If you agree with this pattern I think we should adopt a gentleman's agreement that we each publish a low score example solution before the "race to the top of the mountain" should begin in earnest.

I'm still working on my survey and am also busy on another unrelated job, so I might be behind you in developing my pattern code.

Leren
Last edited by Leren on Fri Jun 02, 2017 11:14 pm, edited 1 time in total.
Leren

Posts: 3315
Joined: 03 June 2012

### Re: Crossword Squares

I hope r7c9 was a typo...

Here is Mount Diablo:
Score = 111
-----------------------------
Grid 8 - Sol 1.JPG (19.96 KiB) Viewed 441 times
JPF
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### Re: Crossword Squares

Your grid looks OK, fixed typo. I'm sure you wont "cheat" and look for high scores until I develop my code for this pattern and publish a low score example.

You must have some generalized code to respond so quickly. I code in Visual Basic in Excel, which is slower than other lower level languages like C++, so to speed things up I have to carefully code each pattern to take advantage of every constraint I can, as I fill up the grid. It will be a day or two before I can post a low score example.

Leren
Leren

Posts: 3315
Joined: 03 June 2012

### Re: Crossword Squares

HI JPF, finally got this pattern working. Here is an example moderate score :

Code: Select all
`---------------------| # A B A N D O N # || A N O X A E M I C || A G # L I B # E R || H O P E F U L L Y || # P E T # T E L # || T H E R E A W A Y || O O # E O N # T O || O R I E N T E E R || K A F S # S A D E |---------------------Score = 118`

I think the appropriate thing to now say is "Gentlemen, start your search engines".

Leren
Leren

Posts: 3315
Joined: 03 June 2012

### Re: Crossword Squares

I find hard to understand these rules where players of a team have the right to enter the field three days in advance to prepare their defense while the opposing team is obliged to remain in the locker room!

Score = 121
-----------------------------
Grid 8 - Sol 2.JPG (19.64 KiB) Viewed 408 times

JPF
JPF
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### Re: Crossword Squares

Code: Select all
`---------------------| # A Q U I V E R # || P R I N C O X E S || A H # W E M # J A || S Y B A R I T I C || # T E T # T E G # || W H E E Z I N G S || A M # R A V # I O || N I N E P E N N Y || K A E D # S A G A |---------------------Score = 149`

Leren

<edit> New high score .... 150

Leren
Leren

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### Re: Crossword Squares

The advantage of this pattern is to prove that my program is bugged. For any pattern it quickly finds a solution - it was its initial purpose - but doesn't find all of them.
I need to work on that which will take a while.

JPF
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### Re: Crossword Squares

Hi JPF,

My method is to code each pattern separately, which is why it takes me a few days to respond to each new pattern.

Whilst the code is similar in each case you have to think carefully about the order in which you fill up the grid. If you make a bad choice your code can be very slow. For this pattern I had to make a few starts before I found a satisfactory way. The trick was to start with the 7 letter word at the top. If you don't do that first, you will run into trouble. I think you also had trouble with one of the earlier patterns that also had 7 letter words.

My code will find all solutions (if there are no bugs), but I also add filters to jump over solutions that I think will be low scoring eg various combinations of rows and columns should have minimum values.

The filtering process is more an art than a science, (because high scores can possibly occur in counter-intuitive situations), which adds to the enjoyment of the overall process.

I'll be amazed if a score over 150 is found for this pattern, the reason possibly being that a 7 letter word and a 9 letter word are in adjacent rows. I've found two separate ones after many days of looking and I think I'll stop there for this pattern.

Leren
Leren

Posts: 3315
Joined: 03 June 2012

### Re: Crossword Squares

Here is my final post on that last pattern. I found four cases with a score of 150 as follows:

Code: Select all
`---------------------  ---------------------  ---------------------  ---------------------| # A Q U I V E R # |  | # F U N K I N G # |  | # F U E H R E R # |  | # L I Q U A T E # || U N I N D E X E D |  | J A P A N N E R S |  | P A R Q U E T E D |  | B E D U N C I N G || P A # H E N # F A |  | U R # V A S # A Y |  | A R # U T U # F Y |  | A H # A T T # R E || O P T O M E T R Y |  | D E M I P I Q U E |  | M E G A S P O R E |  | P R E C O I T A L || # H A N # F E E # |  | # B A C # N U N # |  | # B A L # T W A # |  | # J A K # V A G # || J A R O V I S E D |  | F O R E R E A C H |  | D O M I N A N C Y |  | B A S I F I X E D || A S # R U C # Z A |  | A X # R A W # H E |  | E X # Z E K # T O |  | O H # S A Z # D I || W I N E M A K E R |  | Z E I T G E B E R |  | B E J E W E L E D |  | G R O M W E L L S || S C A D # L Y S E |  | E S T S # D I D Y |  | T S A R # S I D H |  | Y E W S # D I Y A |---------------------  ---------------------  ---------------------  ---------------------Score = 150 One of 135  Score = 150 1 of 5    Score = 150 One of 2   Score = 150 One of 16`

If there is a score of > 150 in there I'm sure I'll never find it. Leren
Leren

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Joined: 03 June 2012

### Re: Crossword Squares

Good job!
I'm off for the moment.

JPF
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