Problem Description

The teacher on a Halloween field trip with her small class, asked the students to guess the number of pumpkins in a pile. Monica guessed 26, Nicole guessed 24, Oleg guessed 25, Paige guessed 22, and Quentin guessed 22. Two were off by 3, two were off by 1, and one guessed the exact number. How many pumpkins were in the pile?
 

Background & Techniques

The above is an example of a class of puzzle which appears quite often in my Mensa Puzzle-A-Day calendar.  

 Solutions to these puzzles may be easier to find manually that it was to write the program to find them automatically.  It took several starts before I came up with the algorithm (algorithm = technique or method) to solve them.  Aristotle said "Well begun is half done" and in programming, the data structure chosen to represent the real world conditions defines that beginning.  The one I ended up with represents the puzzle in a grid with guesses as columns and errors as rows.  The cell at the intersection of each guess and error contains the answers which could reflect that combination.  So for example if one of the guesses was 26 and one of the errors conditions was "off by 3", then that intersection would contain the values 23 and 29.     When the grid is filled in, one of the numbers in the first column must be the correct answer and that same value must appear in a unique row in each of the other columns.   Here is the grid for the above problem from which we can find by inspection that 25 is a correct answer.

 The program follows this procedure, although it takes more code than one would think to do something that is quite simple for a human.  For example when checking column 5 for the guess value 25, we need to make sure not to check row 1 (even though it contains a 25 in column 5) since we have already used that row.  Humans can do this without setting up a nested loop to check all of the columns ahead of the current column.  (Or maybe we do without being aware of it.  Anyway, it seemed like being a human was a big advantage when solving the first puzzle of this type.  For all future puzzles however, the computer has a definite advantage!)

In addition to a "Solve" button, there is a "Change" button that lets the user change or define new problems, to load any of several sample problems that are to included, and to save any changes made to a file.

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

Notes for programmers

To implement the above method, I defined a TErrType record type to keep the error value and the direction, too high (+), too low (-) or "off by" (±).    An array of these records represents the error values for the rows in the grid.  A TGuessRec defines the possible actual values for each guess and error value combination  (as integers Upval and Downval).  A two dimensional array of these records is the internal representation of the data displayed in the TStringGrid that the user sees (and the grid displayed above).   

All the good stuff happens in the SolutionBtnClick procedure. It runs through all the unique possible actual values for the first guess ( the first column).  For each, it calls a local function, Goodval, which checks whether the potential actual value is a solution. and returns Boolean value "True" if it is, "False" otherwise   The value is a solution if, for each column after the first, the value appears  in some unused row as an Upval or Downval for this column.   Failing to find a value for nay column causes the function to return "false".  When Goodval returns true, local procedure ShowSolution displays the result.

The other button on the main program form , Change, moves the puzzle data to three TMemos in Editform named GuessData, ErrorData, and StoryData and calls ShowModal to display the form.   The user may replace any or all of this data.  When he clicks the OK button, the data is validated before returning to the main form with a return code of MROK.  If an error is found, a message is displayed and the return code is set to MRNone which prevents the exit.  Save and Load buttons use the CommaText property of Tmemo.Lines stringlists to save and restore the data, preserving line structure.   

Running/Exploring the Program 

Suggestions for Further Explorations

 There are probably smarter ways to solve the puzzle (for example, if we are told that one of the guesses is correct, the number of possible correct values to check could be reduced to the given guess values.)  Or perhaps pass the guesses against the errors instead of the current method which passes errors against the guesses.

A game generator make a good project add-on.   I suspect that puzzles more difficult than the current sample set could be developed.   I would make a file of proper names for the guessers and  a file of container/object pairs to randomly select from.  Then the program could specify the number of guessers, their accuracy (10%, 20%, etc. maximum error), and the correct answer.  We could then generate the guesses, the errors, and even  the story text with the help of Delphi's  random number  generator.