Material From REC


Recreational & Educational Computing is a 14 to 18 page newsletter published 6 times a year by Dr. Michael Ecker.

REC Focus: Stimulating mathematics, recreation, education, programming, graphics, and other computer activity.

Dr. Ecker has several subsidiary programs to compliment REC, such as:
        REC-on-Disk which includes the paper version plus all programs plus additional material
        Mathematical Farragoes each of which are multiple disk collections of contributed programs.

I thank Dr. Ecker for permission to show here several magic squares previously published in REC.
And , of course, I thank the authors for their ingenuity and hard work.

Editor note: In 2010 the REC web site at aol was no longer available and I have lost touch With Dr. Ecker.

Order-5 Palindrome Magic square Order-4 and order-5 magic squares consisting only of palindromes.
Consecutive Prime Numbers Order-9 An order-9 magic square consisting of 81 consecutive primes.
Forty-one This order-11 magic square includes 41 fortyones.
E. S.-71 This order-16 magic square includes the authors initials and year of construction.
Number-Nine Magic Square An order-4 magic square changed into an order-5 by adding 8 additionaal nines.
Order-16 Prime Number Magic Square With inlaid orders 4, 6, 8, 10, 12, 14 magic squares of primes.
Order-6 Prime Magic Star This star uses 19 consecutive prime numbers in 9 lines of 5.

Order-5 Palindrome Magic square

Written to celebrate the palindromic year 1991., the 25 palindromes of this order-5 square have the magic sum 1991.

Adding 11 (another palindrome) to 1991 gives the next palindrome year 2002, the sum of this order-4 magic square. It consists of 16 different palindromes

Alan W. Johnson, Jr., REC vol.5,  No. 8. December 1990,Page 4

Consecutive Prime Numbers Order-9

This order-9 magic square is composed of the 81 consecutive prime numbers 43 to 491. The magic sum is the prime number 2311.

Alan W. Johnson, Jr., REC vol. 7 No. 7. February1993,Page 10


This order-11 magic square consists of a normal order-9 composite magic square divided into it's nine order-3 magic squares with 40 additional forty-ones. The magic constant is 11 x 41. Mr. Shineman constructed this square to celibrate the year 1941!

The magic constant of each of the nine order-3 magic squares themselves form an order-3 magic square, a feature of all composite magic squares.
The principal holds for any number substituted for 41, as long as the starting number is such that the middle number of the series is the number you wish to substitute for 41.

E. W. Shineman, Jr., REC  vol.8 No. 1 & 2. July 1993,Page 5



E. S.-71

This order-16 magic square is pandiagonal so broken diagonals also sum to the constant 2056, as well as each of the authors initials and the two figures of the year of creation (1971).

It may also be considered an ornate magic square because of the inlaid figures (E, S, 7 and 1).
Of course, if you make use of the pandiagonal feature to tranform it to a different magic square by moving columns or rows from one side to the other , this   ornate feature would disappear.

E. W. Shineman, Jr., REC  vol.8 No. 3 & 4. July/August/September 1993, Page 17

Number-Nine Magic Square

An order-5 magic square constructed from the series of numbers from 1 to 17, but with 8 additional (total of 9) nines .

The magic sum = 45. Note that 9 = 4 + 5 which is also the two orders involved. Also, the outer four order-2 squares are not magic but the four cells of each sum to 36 and 3 + 6 = 9.

This is classified as an ornate magic square. It is not a pure or normal one because it doesn't consist of a series of numbers from 1 to n2.

E. W. Shineman, Jr., REC vol.10 No. 3 & 4. December 1995-January 1996,Page 1

Order-16 Prime Number Magic Square

This magic square contains inlays of each even order magic square from 4 to 14. It looks like a concentric or bordered magic square, but this square has the low and high numbers scattered throughout the square. With a  true bordered magic square, one half  the numbers in the border consists of the low numbers in the series, the other half are the high numbers.

Here each square has all rows, columns and main diagonals equal to the magic constant for that square.

The magic sums differ by a constant 2730.

Alan W. Johnson, Jr., REC vol.6, No. 1 & 2. March 1991,Page 13

Order-6 Prime Magic Star

This magic star uses the prime numbers from 3 to 71. Each of the 9 lines of 5 numbers sums to the prime number 167.

This is an unusual example of a magic star. Generally, a magic star is considered to have four numbers per line.
Much more on this subject is in my Magic Stars section of this site.

Alan W. Johnson, Jr., REC vol.15, No. 2 & 3. Winter 2000-Spring 2001, page 21


This page was originally posted June 1998
It was last updated July 19, 2010
Harvey Heinz
Copyright 1998-2009 by Harvey D. Heinz