Jebreel-smarandache Fractional Magic Square

Smarandache Fractional Magic Square By: Muneer Jebreel Karama SS-Math-Hebron Field Education Officer Jerusalem .box 19149 [email protected] Abstract The aim of this paper is to present new Smarandache magic squares related to fractions, and present an open question. Key words Magic square, Smarandache Fractional Magic

Square. Definition : Smarandache Fractional Magic Square is consists a of the distinct fractions ( , where the greatest common b

divisor of a and b equal 1 i.e. relatively prime ) such that the sum of fractions in any horizontal , vertical , or main diagonal is always the same magic constant which is integer . Examples:

67 8

7 6

155 24

41 12

16 3

29 4

101 24

19 2

55 24

Figre.1

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We note that in figre.1 , each column, each row, and both diagonals sum to 16.

61 8

5 6

133 24

31 12

14 3

27 4

91 24

17 2

41 24

Figre.2 We can note that in figre.2 , each column, each row, and both diagonals sum to 14. Also, if we sum the corresponding cells in figre.1 and figre.2 we obtain the following magic square as in figre.3:

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16

2

12

6

10

14

8

18

4

Figre.3 Open Question: Are there a Smarandache Fractional Magic square such that the denominator and numerator are prime numbers.

Reference:

[1] M. Jebreel Karama , Smarandache concatenated magic square, Smarandache Notions Journal, Vol. 14 , 2004, 80-83. [2] http://www.gallup.unm.edu/~smarandache

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