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There Are Magic Hexagons of Every Order

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Re: There Are Magic Hexagons of Every Order

#5

Post by gukoff »

amelius wrote: post #4

Why is not every 45 degree line considered for the rectangular grids? (In the hexagons, all lines are considered even if they don't have the maximum length) (PS: make sure you hover your mouse over the diagrams)

Interesting observation. That's simply part of the usual definition of a magic square, and it does indeed feel arbitrary once you compare it with the hexagon case, which is very symmetrical. I first learned about magic squares from math books as a kid, about 25 years ago, and just accepted those rules as given.

Upon a quick research, there are many variations, and the closest to what you're describing is the "pandiagonal" magic square, where additional diagonals are considered (except they wrap around the edges of the square in a slightly funny way, so that every diagonal still contains exactly N numbers): https://en.wikipedia.org/wiki/Pandiagonal_magic_square

Re: There Are Magic Hexagons of Every Order

#7

Post by bluedragon1221 »

chrystalkey wrote: post #6
sublinear wrote: post #3

Earlier quoted context omitted.

CGP Grey is never coming back

Right probably. Do you know what happened by any chance?

Not sure. He quit his podcast (Cortex) saying it was "time for a break." Now Myke runs the show by himself

Re: There Are Magic Hexagons of Every Order

#8

Post by Sharlin »

amelius wrote: post #4

Why is not every 45 degree line considered for the rectangular grids? (In the hexagons, all lines are considered even if they don't have the maximum length) (PS: make sure you hover your mouse over the diagrams)

The shortest 45 degree line in a magic square is a single cell, making it somewhat tricky to add up to the same total as the other lines.
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