Scrambled Pie Puzzle

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As of October, 2016, Embarcadero is offering a free release of Delphi (Delphi 10.1 Berlin Starter Edition ).     There are a few restrictions, but it is a welcome step toward making more programmers aware of the joys of Delphi.  They do say "Offer may be withdrawn at any time", so don't delay if you want to check it out.  Please use the feedback link to let me know if the link stops working.


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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

Mensa® 365 Puzzlers Calendar 2018

(Hint: If you can wait, current year calendars are usually on sale in January.)


Feedback:  Send an e-mail with your comments about this program (or anything else).

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Problem Description

Given a set of 4 partial words, each missing then same single letter, identify the missing letter and unscramble the words.

Background & Techniques

This puzzle is a type that occurs occasionally in  the Mensa® Daily Puzzle Calendar.   It is logical combination of of two programs already included in Wordstuff2: Unscramble which unscrambles word anagrams, and Crossword Helper, which fills in missing letters in partial words.   

Solving the puzzles is essentially an offline exercise, not much need to tell the computer the words once you have found them.   But it will generate new puzzles for you at several levels of difficulty.  Levels 1 through 4 choose from words increasing length.  By loading larger dictionaries,  puzzles generated at each level become much harder to solve.   The default dictionary (Small.dic) contains less than 2000 words for the program to choose from.  General.dic contains about 17,000 words and Full.dic has about 62,000 words!  The pie image above is a typical  level 1 puzzle generated with Full.dic.   Not an easy puzzle although there are at least two choices for the missing letter.

The program will also solve puzzles that it generates (wow!) or that you enter manually (if, for example, you can't solve a Mensa calendar version and for some reason don't want to turn the page to find the answer).

.Non-programmers are welcome to read on, but may want to skip to the bottom of this page to download executable version and the dictionaries for this program. 

We had four main problems to solve in writing the program:

  1. Program Logic - finding the solution when then user clicks the "find it for me" button

    I  modeled Scrambled Pie after Unscramble with two changes in the logic - we don't have to worry about generating two and three word phrases from the scrambled letter, which simplifies things a lot.  But because the missing letter is unknown, we append all possible letters to each of the partial words and then look for a letter that produced anagrams of valid words in all four cases.

  2. Drawing the pie figure.

    A TImage provides the canvas for the pie.  The interesting part was placing the letters randomly with each quadrant without overlapping each other or the borders of the quadrant.  I used polar coordinates to randomly select and angle in the appropriate quadrant for the current word (a) and a distance (r) from the center.  For each (r,a) pair, convert back to Cartesian (x,y), determine the pixel size of the current letter and see if this rectangle overlaps either another quadrant or another letter that has already been placed in this quadrant.   If so, try again until a good position is found.   

  3. Printing the puzzle text and graphics

    Printing is always harder than it seems it should be.  Because printer resolution is several times higher than monitor resolution, drawing the canvas to the printer produces a very small image, and stretching the display canvas to the printer canvas size produces a lousy (low resolution) image.   The only solution is to  rerun the code that drew the original image to the monitor using the printer canvas instead.   This means that the drawing routines must have "Canvas" as a parameter.  One other note - the font "PixelsPerInch" property must be set to printer resolution  if necessary.  The pie part of the image is drawn to a temporary bitmap which is then copied to  the printer canvas.  The temp bitmap canvas needed to know that the resolution was high so that the TextOut procedure could use more pixels while drawing the letters.   

  4. Printing the solution words up-side down at the bottom of the page.

    Inverted text problem was interesting enough that I wrote a separate test program and posted it over in Delphi-Techniques at  Inverted Text.  

All-in-all, there's plenty enough non-trivial code here to put this program in the advanced category.    And there are only a couple of these puzzles in each year's Mensa calendar (and the answer to those can be obtained by flipping the page over).  So I guess we've proved once again that the journey is more important that the destination! 

Running/Exploring the Program 

bulletDownload source
bulletDownload  executable
bulletDownload Dictionaries  (required one time, either from here or  with Wordstuff2 programs)

Suggestions for Further Explorations

It would be smart of the program to automatically switch to a higher level dictionary when solving a user entered puzzle and no solution is found using the current one.  (And switch back to the user selected dictionary after the search.)
Difficulty levels could be added by associating a dictionary as well as a range of word sizes with each level. 
A test should be made for duplicate words after a puzzle is generated.  I have seen a case where the same random word was selected twice in the same puzzle.   
Wordstuff2 is a "wrapper" for five previously written programs which use the dictionary unit.  Scrambled Pie should logically be the sixth. 



Original Date: April 6, 2004 

Modified: July 29, 2017

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