Digit tree Puzzle

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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.)


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Problem Description


Place the digits 1 through 9 in the circles at right so that the value in any circle will be the sum of the digits in the circles connected from below.

Background & Techniques

Here is the second little puzzle program adapted from my most recent puzzle book acquisition,  Giant Book of Mensa Mind Challenges , Stirling Publications, 2003.   

The operation of the program is simple:  Drag digits to the circles until the conditions are satisfied.  Clearly, since there are nine digits and only seven circles, some of the circles will contain two digits.  Drag and drop digits on the left or right side of the circle, depending whether you are setting the left or right digit. 

The solution is not included as part of the program but if you really get stuck, I have included it as a sample problem with our Brute Force problem solver which uses exhaustive search to find solutions for a given set of equations and values.     

From the programming point of view, the coding techniques are similar to those used in the Added Corners puzzle, the only real complication being the requirement to keep track of the possibility  two digits in a circle and evaluating them appropriately when forming sums.    

Addendum Sept 21, 2010:   Here's Version 2 version with a "Hint" button added.  Each click will remove an entry in the incorrect position or briefly show an unplaced number in the its correct location.      

Running/Exploring the Program 

bulletDownload source
bulletDownload  executable

Suggestions for Further Explorations

I wonder,  how many other graphs could be created using the 9 digits with other arrangements of circles and meeting some mathematical condition?   


Created March 1, 2006 

Modified: May 15, 2018

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