# Thread: Sarah's Key

1. ## Sarah's Key

This may be an ever expanding mathematical riddle. You solve one, we get to move on to the next level.

The history of the 3x3 magic square goes way back. Chinese legends concerning the pre-historic Emperor Yu (夏禹) tell of the Lo Shu, often in connection with the Ho Tu (河圖) figure and 8 trigrams. In ancient China there was a huge deluge: the people offered sacrifices to the god of one of the flooding rivers, the Lo river (洛水), to try to calm his anger. A magical turtle emerged from the water with the curious and decidedly unnatural (for a turtle shell) Lo Shu pattern on its shell: circular dots giving unary (base 1) representations of the integers one through nine are arranged in a three-by-three grid. http://en.wikipedia.org/wiki/Lo_Shu

There is only one unique solution to the 3x3 magic square. Since we have 10 fingers (digita = Latin), wouldn't it be nice to find a home for the 0 digit? Tell me where you think is the best place for the 0 in relation to the other nine and why.

Happy sleuthing,
Steve

2. Originally Posted by Ps 27:1
This may be an ever expanding mathematical riddle. You solve one, we get to move on to the next level.
How exactly do we know when we've "solved" of riddle that hasn't been stated? It sounds like the riddle has itself become a riddle! Riddles within riddles ... guess we are ensured of eternal fun, anyway. That is, if you like puzzles and all.

Originally Posted by Ps 27:1
The history of the 3x3 magic square goes way back. Chinese legends concerning the pre-historic Emperor Yu (夏禹) tell of the Lo Shu, often in connection with the Ho Tu (河圖) figure and 8 trigrams. In ancient China there was a huge deluge: the people offered sacrifices to the god of one of the flooding rivers, the Lo river (洛水), to try to calm his anger. A magical turtle emerged from the water with the curious and decidedly unnatural (for a turtle shell) Lo Shu pattern on its shell: circular dots giving unary (base 1) representations of the integers one through nine are arranged in a three-by-three grid. http://en.wikipedia.org/wiki/Lo_Shu

There is only one unique solution to the 3x3 magic square. Since we have 10 fingers (digita = Latin), wouldn't it be nice to find a home for the 0 digit? Tell me where you think is the best place for the 0 in relation to the other nine and why.

Happy sleuthing,
Steve
Hummm ... I'm clueless on this one. Why would it be nice to find a place for the zero? I guess we could put it everywhere, in the form of n + 0 for each of the squares. Or we could use n x 0 and have fun with a magic square where all the rows, columns, and diagonals sum to Zero! The Void! How Buddhist of us, eh?

3. Originally Posted by RAM
How exactly do we know when we've "solved" of riddle that hasn't been stated? It sounds like the riddle has itself become a riddle! Riddles within riddles ... guess we are ensured of eternal fun, anyway. That is, if you like puzzles and all.
Don't rain on the parade just yet. I like that: "The riddle has itself become a riddle!"

Hummm ... I'm clueless on this one. Why would it be nice to find a place for the zero? I guess we could put it everywhere, in the form of n + 0 for each of the squares. Or we could use n x 0 and have fun with a magic square where all the rows, columns, and diagonals sum to Zero! The Void! How Buddhist of us, eh?
Are you doing this already?

Answers: It's a riddle, no, and no.

Steve

4. Originally Posted by Ps 27:1
Don't rain on the parade just yet. I like that: "The riddle has itself become a riddle!"
Yeah ... me said a funny!

Originally Posted by Ps 27:1
Are you doing this already?

Answers: It's a riddle, no, and no.

Steve
I don't know ... maybe. Maybe not. Do I get a clue?

The 3 x 3 magic square is cool. All the even numbers are in the corners, and the five odd numbers make the pattern of a cross like in the Chinese representation of the number 5 in the center of the five odd numbers in their magic square:

The solid circles are the evens, the unfilled circles are the odds.

All the numbers opposite each other add to ten. The central number is 10/2 = 5.

5. Originally Posted by RAM
Yeah ... me said a funny!

I don't know ... maybe. Maybe not. Do I get a clue?

The 3 x 3 magic square is cool. All the even numbers are in the corners, and the five odd numbers make the pattern of a cross like in the Chinese representation of the number 5 in the center of the five odd numbers in their magic square:

All the numbers opposite each other add to ten. The central number is 10/2 = 5.
I actually already gave you a clue.

Usually at the beginning of the semester of my math classes, I would give them some riddles. The one that would always stump them was: pick up a rope in each hand and tie a knot without letting go of either end and have no body parts inside the knot. They would eventually swear that it could not be done. I would often times stand in front of them with my arms crossed, because that is how you solve the riddle.

Steve

6. Okay, second part to this riddle. PI is one of the most important numbers in mathematics, agreed? Give an algorithm, simple enough for a child to understand, that uses all of the magic square to get 3142. (PI to the nearest thousandth ignoring the decimal.) Kind of like a pin number.

Bonus points if you can extend the string, 314159...

Steve

7. Originally Posted by Ps 27:1
I actually already gave you a clue.
This is fun! I haven't engaged in a riddle challenge for a long time. Now I'll have to psychoanalyze you so I can guess what kind of answers you are expecting. "Find a home for the 0" ...

Originally Posted by Ps 27:1
Usually at the beginning of the semester of my math classes, I would give them some riddles. The one that would always stump them was: pick up a rope in each hand and tie a knot without letting go of either end and have no body parts inside the knot. They would eventually swear that it could not be done. I would often times stand in front of them with my arms crossed, because that is how you solve the riddle.

Steve
That crossed arm trick is great! I had never heard of it before.

Now I'll go back and see if I can discern your riddle. Which post was the clue in?

8. Originally Posted by RAM
Now I'll go back and see if I can discern your riddle. Which post was the clue in?
You're killing me!!

Okay, I'll play nice. Which post did I put it in?

I know. I originally put it in one of them but then I inadvertently put it in all of them!

Steve

9. Originally Posted by Ps 27:1
You're killing me!!

Okay, I'll play nice. Which post did I put it in?

I know. I originally put it in one of them but then I inadvertently put it in all of them!

Steve
Well, the thing about riddles is that they can be very idiosyncratic.

OH - I think I get it. You would draw a circle around the magic square, right?

Just like this image from the Lo Shu page you linked:

10. Originally Posted by RAM
Well, the thing about riddles is that they can be very idiosyncratic.
In spite of the fact that I have been euphemistically called eccentric and labeled a narcissist, you might like the answer.

OH - I think I get it. You would draw a circle around the magic square, right?

Just like this image from the Lo Shu page you linked:
You're getting warmer, but, no.

Steve

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