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.