The grid to the left is cyclical over 4 rows and 4 columns. A 4 x 4 grid, when suitably selected and appropriately overlaid upon the left grid with their matching cells added, becomes a panmagic square.

		A	B	C	D	E	F	G	H	I			P	Q	R	S	T	U
	a	13	11	16	6	21	11	6	15	27		p	5	1	14	10	5	1
	b	10	19	9	16	13	10	19	17	13		q	6	5	9	11	6	5
	c	13	25	7	6	21	9	13	8	13		r	12	16	15	4	12	16
	d	9	10	5	19	9	20	14	18	8		s	8	7	2	13	8	7
	e	16	12	23	9	16	11	6	16	26		t	5	1	14	10	5	1
	f	18	14	15	18	13	10	19	17	13		u	6	5	9	11	6	5
	g	6	25	13	6	13	9	13	8	9
	h	15	20	14	19	8	20	14	18	8
	i	9	11	6	9	27	11	6	16	27
	j	18	19	16	18	8	19	17	13	8

Tell me:
1. the magic constant of your grid
and
2. the two cells which overlapped to form the top left corner of your newly formed grid, eg: Bb and Qr.

That example, Bb and Qr above, would choose the subsets:

Bb	19	9	16	13			Qr	16	15	4	12				35	24	20	25
	25	7	6	21		+		7	2	13	8		=		32	9	19	29
	10	5	19	9				1	14	10	5				11	19	29	14
	12	23	9	16				5	9	11	6				17	32	20	22

of which the latter is NOT a magic square.

Oh! And be careful that any magic square chosen is in fact Pan Magic!

Other than rows, columns and major diagonals, the following arrangements, as well as their rotations also form the magic constant.

The following definition extracted from wikipedia applies here (and is demonstrated by the first two 4 x 4 grids above).

A panmagic square is a magic square with the additional property that the broken diagonals, i.e. the diagonals that wrap round at the edges of the square, also add up to the magic constant. http://en.wikipedia.org/wiki/Panmagic_square

1. magic constant = 90

2. Ordinary grid begins with Bc and Qq, and the special case uses Ef and Qq.

Edited on September 25, 2023, 8:31 pm

Posted by K Sengupta on 2023-03-24 04:17:56