Thread: A magic square?

Hi guys.

A challenge for you all: This is the third forum I'm trying, and thus far the squares below remain unsolved. It is my hope that this forum will change that!

Attached are two number grids. One is a 10X10 and and contains numbers 0-9. The other is a 12X12 and contains number 1-12. The squares come from different puzzles, but by the same author (I included both as one square is complete, and may give a clue as to how the other is compiled)

The puzzles both bare no copyright, and form part of a geocaching puzzle (see Geocaching - The Official Global GPS Cache Hunt Site).

By filling in the numbers on the 10X10 square one should be able to obtain a set of GPS coordinates. As we are in Cape Town, South Africa, the numbers will probably look like this: (S33[or 34] XX.XXX ; E18 XX.XXX)

Just for interest sake the 12X12 square puzzle came with the following clue which would also reveal a GPS coordinate as for the above:
S 34° [9(1) - 9(2)] [7(4)] . [2(2)] [6(2)] [7(3)]
E 018° [6(1)] [4(2)] . [4(1)] [9(4)] [1(4)]


Wishing you all the best and may thanks

Originally Posted by doceave

....and thus far the squares below remain unsolved.

Attached are two number grids. One is a 10X10 and and contains numbers 0-9. The other is a 12X12 and contains number 1-12.

No wonder it remains unsolved: you've attached the 10by10 twice, and no 12by12 !

My apologies... here is the 12X12.... (Still not necessary for solving the 10X10)

Simple brute force will work on the 10x10 because there are at most 10^10 operations, and the main issue would be how long it takes to enter the data. 10^10 is already fast enough, but if enhanced by backtracking, the algorithm will run plenty fast.

For the 12x12 there is some trick since the square is already filled in, and presumably it relies on the other clue you gave; my guess would be that 9(1) stands for either the position of the 9th occurrence of 1, or the first occurrence of 9, or the entry in the 9th row and first column, or some such. Since you are familiar with reasonable coordinates, how about try out some such guesses and see if any produces a sensible result.

Originally Posted by undefined

For the 12x12 there is some trick since the square is already filled in, and presumably it relies on the other clue you gave; my guess would be that 9(1) stands for either the position of the 9th occurrence of 1, or the first occurrence of 9, or the entry in the 9th row and first column, or some such. Since you are familiar with reasonable coordinates, how about try out some such guesses and see if any produces a sensible result.

Hi there Undefined (cool profile pic ~ HDR?)
I have already tried that which you suggest... Once i have counted, for example the 9th occurance of 1 or the inverse, I still do not know what to do next ~position of the block from the start / sum of row + columns / position of block from end...

The only clues I can see are in the formatting: [9(1)-9(2)] must equal 1 digit. Likewise [7(4)] must equal 1 digit.

9(1) > 9(2) as you cannot have a negative value here.
Values [2(2)] ... [6(2)] ... and [7(3)] must all be single digit...

Ok I let me test the above and see if it helps find a pattern.

But please. Anyone with any smarter ideas please do share! Thanks for help thus far.

For the 10x10, brief analysis reveals the magic sum must be 44. This makes it easy to do on paper.

What does HDR stand for?

Yeah for the 12x12, I don't know there's a definitive answer, and if all coordinates from 000.00 to 999.99 make sense, then I think it's just guessing..

@Undefinded: The only definites in the co-ords are S34 xx.xxx and E18 xx.xxx

@Undefinded: HDR ~ High Dyanmic Range... Really awesome spin on digital photography where you take three images of the same thing at different exposure levels then combine them to get massive pixel depth (and indeed pick up more detail than the human eye in anygiven light! - if done properly)

As for the 10X10... I really don't see how the all the rows / columns could add up to 44 where there the bottom row adds to 52 incompleted! Ok you could add a negative number... Could you elaborate as to how you derived 44?

Originally Posted by doceave

@Undefinded: HDR ~ High Dyanmic Range... Really awesome spin on digital photography where you take three images of the same thing at different exposure levels then combine them to get massive pixel depth (and indeed pick up more detail than the human eye in anygiven light! - if done properly)

As for the 10X10... I really don't see how the all the rows / columns could add up to 44 where there the bottom row adds to 52 incompleted! Ok you could add a negative number... Could you elaborate as to how you derived 44?

I assumed the square was well constructed, so obviously it's not.

Not counting the question marks, the first row adds to 41, the last column adds to 35, and the second row adds to 44.

So the maximum is 35+9 and the minimum is 44+0, so it's 44, but maybe you shouldn't do this challenge since the challenger doesn't seem to be very careful checking for errors and ambiguities.

Or, did the original problem say "magic square" anywhere in it? Because if not then the title of your post is misleading everyone.


That's cool about HDR, but I just took the image off some free wallpaper site or something, I have the larger image somewhere on my computer.

Edit: Come to think of it, the fact that the first row and last column have different sums should have tipped me off, I just wasn't paying attention and was operating under the notion that the problem made sense..

@Undefined: There is no error ~ this is the work of a genius! Both puzzles have been solved 100+ times over the past 6 years. Title was "number cruncher" or something to that effect.

There are, or at least I have tested, 8 different types of "magic square" and have yet to find one that it conforms to. Hence my title ~ "A magic square?"

I will find youa link of a 360degree photo I took in HDR.... Ahh here it is: http://www.doceave.com/panoramics/gs...highq_tour.swf Pic taken in too-dim-to-read light...

Originally Posted by doceave

@Undefined: There is no error ~ this is the work of a genius! Both puzzles have been solved 100+ times over the past 6 years. Title was "number cruncher" or something to that effect.

There are, or at least I have tested, 8 different types of "magic square" and have yet to find one that it conforms to. Hence my title ~ "A magic square?"

I will find youa link of a 360degree photo I took in HDR.... Ahh here it is: http://www.doceave.com/panoramics/gs...highq_tour.swf Pic taken in too-dim-to-read light...

Well titling the post "A magic square?" can give a few different ideas:

(1) Here is a square that I'm guessing is magic
(2) Here is a magic square I cannot solve

Without thinking, I thought (2) was meant, and didn't bother looking for other interpretations.

Another idea for 10x10 is to look for common/"famous" decimal expansions, like pi or e or sqrt(2); haven't found anything so far.

That panoramic photo is quite nifty!

@Undefined: Title describes my thoughts and is appropriate. This could very well be an exotic magic square. Magic Square -- from Wolfram MathWorld

Over a hundered of the buggers described! Def not any sqaures of centre digits or pi... numbers are way to small and number like 7 just dont fit into those well.

WRT the HDR 360: If you let the image load completely you will be able to click a link on the roof taking you to the same image with myself stitiched in... Next one is my wife making a horror movie pose!

Originally Posted by doceave

@Undefined: Title describes my thoughts and is appropriate. This could very well be an exotic magic square. Magic Square -- from Wolfram MathWorld

Over a hundered of the buggers described! Def not any sqaures of centre digits or pi... numbers are way to small and number like 7 just dont fit into those well.

WRT the HDR 360: If you let the image load completely you will be able to click a link on the roof taking you to the same image with myself stitiched in... Next one is my wife making a horror movie pose!

The standard notion of magic square has all rows and columns with equal sums, and sometimes diagonals too, so you should not find it hard to believe your title can mislead people.

If you want to be nice to the people trying to help, then say things like "I have verified that this is not a standard magic square because the rows and columns can't possibly all have the same sum", etc. Otherwise you are wasting our time by making us rediscover the things you already know.

A new, non-magical, much less deceptive thread created above!

Originally Posted by doceave

A new, non-magical, much less deceptive thread created above!

Mmmm, you mean well, but it's against the rules to create a duplicate thread, as it clutters the forum. Cross referenced so that the mods can clean it up..