Find 3 Primes

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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

Here's a simple little program to solve this problem:  "There is only one set of 3 different two-digit prime numbers with the property that the mean of any two number and of all three are all also prime.  What are the numbers?"

Background & Techniques

There are only  21 two digit primes, so we'll build a array containing them and then select all subsets with 3  numbers to check if the means are also prime numbers.  The mean of any set of n-digit positive integers lies between the smallest and the largest so will also be an n-digit number. This lets us just check if the means are integers and in the 2-digit table of primes. 

 Procedure MakePrimes builds the table of primes by checking integers 11 through 99 that no smaller prime divides  it evenly.  It calls function IsPrime to perform this test, (B divides A evenly if (A div B)*B=A where "div" is the integer divide operation which returns an integer quotient ignoring any remainders.)  Function IsPrimeInteger takes a sum. M,  and the number of integers summed, K, as parameters and returns true if K divides M (i.e. the mean is an integer) and M div K is in the array of 2-digit primes.  It returns false otherwise. 

100 or so lines of code make this an Intermediate level program.       

Running/Exploring the Program 

bulletDownload source
bulletDownload  executable

Suggestions for Further Explorations



Original:  November 17, 2010

Modified:  May 15, 2018

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