**HP Prime and Casio fx-CG 50: 3 x 3 Magic Squares**

**Background**

A magic square is a square of integers where each row,
column, and diagonal have the same sum.
For example:

2 |
9 |
4 |

7 |
5 |
3 |

6 |
1 |
8 |

Each row, column, and diagonal of this magic square has a
sum of 15.

A proper magic square has the integers 1 through n^2, n is
the size of the magic square. A
non-normal magic square follows the sum rule, but different integers than the 1
to n^2 sequence is allowed.

The program MAGICSQ3 generates random 3 x 3 non-normal magic
squares. The sum of each row, column,
and diagonal are given.

**HP Prime Program: MAGICSQ3**

EXPORT MAGICSQ3()

BEGIN

// Random Magic Square 3 X 3

// 2017-10-06 EWS

LOCAL x,k,r,mat,s,t,l;

// Initialization

r:=RANDINT(−5,200);

k:=RANDINT(1,3);

l:=MAKELIST(k*X,X,r-4*k,

r+4*k,k);

l:=SORT(l);

s:=ΣLIST(l);

t:=s/3;

mat:=MAKEMAT(0,3,3);

// Generation

mat(2,2):=l(5);

mat(1,1):=l(1);

mat(3,3):=l(9);

mat(1,3):=l(2);

mat(3,1):=l(8);

mat(1,2):=t-mat(1,1)-mat(1,3);

mat(2,1):=t-mat(1,1)-mat(3,1);

mat(2,3):=t-mat(1,3)-mat(3,3);

mat(3,2):=t-mat(3,1)-mat(3,3);

// Tranpose?

IF RANDINT(0,1) THEN

mat:=TRN(mat);

END;

// Results

RETURN {mat,t};

END;

**Casio fx-CG50G Program: MAGICSQ3**

"2017-10-06
EWS"

RanInt#(-5,200)->R

RanInt#(1,3)->K

Identity 3->Mat A

Seq(K*X,X,R-4*K,R+4*K,K)->List
1

Sum List 1->S

S/3->T

List 1[5]->Mat
A[2,2]

List 1[1]->Mat
A[1,1]

List 1[9]->Mat
A[3,3]

List 1[2]->Mat
A[1,3]

List 1[8]->Mat
A[3,1]

T-Mat A[1,1]-Mat
A[1,3]->Mat A[1,2]

T-Mat A[1,1]-Mat
A[3,1]->Mat A[2,1]

T-Mat A[1,3]-Mat
A[3,3]->Mat A[2,3]

T-Mat A[3,1]-Mat
A[3,3]->Mat A[3,2]

If RanInt#(0,1)=1

Then

Trn Mat A->Mat A

IfEnd

"TARGET
SUM:"◢

T◢

Mat A

Note: ◢ = Disps

Your results will vary.
Happy Halloween (one week to go!)

Sources:

Learn-With-Games.Com “Magic
Square Solution” http://www.learn-with-math-games.com/magic-square-solution.html Retrieved October 6, 2017

William H. Richardson.
“Non-Normal Magic Squares.” http://www.math.wichita.edu/~richardson/mathematics/magic%20squares/notnormalmagicsquare.html Retrieved October 22, 2017

Eddie

This blog is property of Edward Shore, 2017.

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