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Thread: Sarah's Key

  1. #1
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    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
    May the words of my mouth and the meditation of my heart be pleasing in your sight, O LORD, my Rock and my Redeemer. Ps 19:14 (NIV)

  2. #2
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    Quote Originally Posted by Ps 27:1 View Post
    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.

    Quote Originally Posted by Ps 27:1 View Post
    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?
    • Skepticism is the antiseptic of the mind.
    • Remember why we debate. We have nothing to lose but the errors we hold. Who but a stubborn fool would hold to errors once they have been exposed?

    Check out my blog site

  3. #3
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    Quote Originally Posted by RAM View Post
    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
    May the words of my mouth and the meditation of my heart be pleasing in your sight, O LORD, my Rock and my Redeemer. Ps 19:14 (NIV)

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

    Quote Originally Posted by Ps 27:1 View Post
    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:

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    Click image for larger version. 

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    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.
    • Skepticism is the antiseptic of the mind.
    • Remember why we debate. We have nothing to lose but the errors we hold. Who but a stubborn fool would hold to errors once they have been exposed?

    Check out my blog site

  5. #5
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    Quote Originally Posted by RAM View Post
    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
    May the words of my mouth and the meditation of my heart be pleasing in your sight, O LORD, my Rock and my Redeemer. Ps 19:14 (NIV)

  6. #6
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    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
    May the words of my mouth and the meditation of my heart be pleasing in your sight, O LORD, my Rock and my Redeemer. Ps 19:14 (NIV)

  7. #7
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    Quote Originally Posted by Ps 27:1 View Post
    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" ...

    Quote Originally Posted by Ps 27:1 View Post
    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?
    • Skepticism is the antiseptic of the mind.
    • Remember why we debate. We have nothing to lose but the errors we hold. Who but a stubborn fool would hold to errors once they have been exposed?

    Check out my blog site

  8. #8
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    Quote Originally Posted by RAM View Post
    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
    May the words of my mouth and the meditation of my heart be pleasing in your sight, O LORD, my Rock and my Redeemer. Ps 19:14 (NIV)

  9. #9
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    Quote Originally Posted by Ps 27:1 View Post
    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:

    Click image for larger version. 

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    • Skepticism is the antiseptic of the mind.
    • Remember why we debate. We have nothing to lose but the errors we hold. Who but a stubborn fool would hold to errors once they have been exposed?

    Check out my blog site

  10. #10
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    Quote Originally Posted by RAM View Post
    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
    May the words of my mouth and the meditation of my heart be pleasing in your sight, O LORD, my Rock and my Redeemer. Ps 19:14 (NIV)

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