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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
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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
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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 |
Forty-one
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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
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E. S.-71
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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
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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
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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
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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 |
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