perplexus.info :: Numbers : PanMagic

PanMagic (Posted on 2007-03-02)

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

Submitted by brianjn

Rating: 3.0000 (2 votes)

Solution: (Hide)

There are two 4 x 4 magic squares within this puzzle, and both have the constant of 90.
The word of caution was imperative as only one fits the "Panmagic" definition.
The 'ordinary' grid begins with Bc and Qq while the 'special' case uses Ef and Qq.
Note:
While I had hoped that this would be solved by 'brute force', Charlie, with his computer program did me a service; originally I had mistyped the first coordinate of the 'special' grid.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Thoughts	K Sengupta	2023-03-24 04:17:56
Overwrite	brianjn	2007-03-14 18:22:39
re: Programming Lessons here.	Charlie	2007-03-13 09:45:00
Programming Lessons here.	brianjn	2007-03-13 06:47:36
computer solution	Charlie	2007-03-03 00:44:17

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (12)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info