Word Grid

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Mensa Daily Puzzlers

For over 15 years Mensa Page-A-Day calendars have provided several puzzles a year for my programming pleasure.  Coding "solvers" is most fun, but many programs also allow user solving, convenient for "fill in the blanks" type.  Below are Amazon  links to the two most recent years.

Mensa 365 Puzzlers  Calendar 2017

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Problem Description

Find the word in this partially filled grid which starts in one corner and circles the board to end in the center square.

Background & Techniques

Here's the puzzle from the January 3 puzzle in "The Brain Game", our daily puzzle calendar for 2013.  (My rule is that I can use any program I have written as a brain extender J!)

"A nine letter word is starts at a corner and spirals into the center. Fill in the missing letters to find out what it is."

For different puzzles, click on the grid to enter edit mode, key in the new changes, then press the "Make templates"  button to exit edit mode and start solving. Click the "Search templates " button to search the dictionary for the matching word.

Non-programmers are welcome to read on, but may want to jump to bottom of this page to download the executable program now.

Programmer's Notes:

For future reference, here are few tips and techniques used in this program .

bulletThe strategy for solving the problem is to generate the 8 possible word templates for words starting each of the 4 corners proceeding clockwise or counterclockwise around the grid before ending with the letter in the center.  Then we'll use our UDict unit to retrieve all 9 letter words in the largest dictionary ( "Full.dic") and check each word against each template looking for those that have matching letters in positions where the letters in the template are known.
bulletIf we make a string of letters and ? characters starting in the top left corner and concatenate (join together) the top row, the last column, the bottom row from right to left and the first column from bottom to top we have the first 8 letter template.
bullet{make a clockwise string around the border from top left corner}
bulletThe corresponding template in the other direction is simply the first template reversed.  Function "ReverseString" in Delphi's StrUtils unit does exactly what we need.  sccw:= reverseString(scw);
bulletTo get the template starting form the next corner, all we must do is move the first two characters to the end of the string. (e.g. s:=copy(s,3,6)+copy(s,1,2);)  Repeat that 3 times, add that center character,   and we have all 4 templates for one direction.  Do the same thing on the reversed string and we'll have the 4 counterclockwise templates.
bulletA dictionary named PubDic is automatically created by the UDict unit.  Function LoadLargeDic is called to load the large dictionary, prompting you for the location if it is not in the same folder as the program.    The dictionary is remembered from run to run in file Dic.ini.  Delete this file to specify a  dictionary from a different location.
bulletA call to Pubdic.Setrange procedure will tell the dictionary that you want to sequentially retrieve all 9 letter words starting with letters "A" though "Z".  Then a "While GetNextWord" loop will retrieve each word and return True until all have been  processed.
bulletWe pass each word retrieved against all 8 templates, discarding any word with a character which does not have the same letter or a ? in the template.  A solution is any word which pass the matching test for all 9 letters.
bulletAn OnDrawCell event exit is used to center the character in the center of each grid cell by placing the top left corner at the center of the cell minus half of the character's width and half the character's height like this:  with rect do textout((left + right - textwidth(s)) div 2, (top + bottom -textheight(s)) div 2, s);
bulletTo allow changes to the grid, the editor features must be enabled but in edit mode the currently selected cell is highlighted and displayed in the default location, distracting for normal usage.  To avoid the distraction when not editing, I added an OnClick event exit with this statement to add the GoAlwaysShowEditor option to the set of grid options when the user clicks on the grid: with stringgrid1 do options:=options + [goAlwaysShowEditor];   The "Make templates" button turns the option off again to restore the normal display by subtracting the option from the set. 

Running/Exploring the Program 

bulletDownload  executable (Includes Full.dic dictionary file)
bulletDownload source  (Note: the UDict unit resides in our library zip file of commonly used units.  Library file DFFVLIB13 or later is required to recompile this program )
bulletDownload current library file (DFFLibV15).


Suggestions for Further Explorations



Original:  January 4, 2013

Modified:  May 15, 2018

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