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  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?

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  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 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.

    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
    I would say the best place for the 0 is in the middle, because then all the numbers add up to 10 instead of 15 and we still have a magic square.

    Rose
    Never trust anything you are afraid to question ~

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  9. #9
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    Quote Originally Posted by Rose View Post
    I would say the best place for the 0 is in the middle, because then all the numbers add up to 10 instead of 15 and we still have a magic square.

    Rose
    Hi Rose! In a true magic square, all the columns, rows, and 2 diagonals must sum the same. But you're not too far off.

    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)

  10. #10
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    Quote Originally Posted by RAM View Post
    Well, you might think you have given clues, but that's not so clear to me. Here is how you stated your riddle:
    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.
    And then when I asked for a clue, you said you had already given one, meaning of course, the original riddle.

    The association between fingers and digits is well known. So maybe you are playing around and suggesting that I need to make a zero with my thumb and forefinger?

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    Good one! I hadn't thought about that, but, no.

    So if you don't want to give any clues, then you might as well "spill the beans." You say that you have given other clues, but I find that very hard to believe looking over your posts. So please state the "several clues" that you have given.
    Where's the smiley for having your arm twisted? Partypooper

    Alrighty then.

    Clue #1 from post #60 in my original thread.

    Quote Originally Posted by Ps 27:1
    One of things I was working on last year was the 3x3 magic square. 505 was the key for me to see deeper riddles in the magic square and the 3x3x3 cube. More about that in another thread. Sarah = 505 (Hebrew).
    Clue #2 My avatar.

    Clue #3 "Wouldn't it be nice to find a home for the 0 digit?

    Thanks!
    You're welcome.

    with sore arm,
    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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