Friday Riddle - EARLY

nudgie
nudgie Member Posts: 1,478 Member
edited March 2014 in Colorectal Cancer #1
I will be out of the office and computerless until Monday, so here we go.................

RIDDLE: How can you arrange four ordinary wineglasses on an ordinary table so that "foot" (center of the bottom of the stem) of each is the same distance from all the others?

Comments

  • kmygil
    kmygil Member Posts: 876 Member
    #2
    upside down
    Arrange the glasses in a circle, upside down?

    Kirsten
  • PhillieG
    PhillieG Member Posts: 4,866 Member
    #3
    I'm missing something I guess
    with a real good ruler or you could even have them touching right side up.
    Or, if you drank all 4 glasses of wine, how would you know the difference or would it even matter?
    ;-)

    Have a great weekend!
    ;-)
  • PGLGreg
    PGLGreg Member Posts: 731
    #4
    Invert 3; balance the 4th on top
    If the 4 feet are to be equidistant, they must be at the vertices of a trapezoid. To form the bottom side of the trapezoid, which is an equilateral triangle, invert 3 of the glasses on the table and place them so the sides of each touches the other two. Then balance the 4th glass upright on the bottoms of the first 3. The center of this 4th glass will be the top vertex of the trapezoid. Now raise the center of the 4th glass by inserting spacers under the bottom of this 4th glass (using coasters, perhaps), until its center is as far from the centers of the other 3 as these other 3 are from each other.
    --Greg
  • PGLGreg
    PGLGreg Member Posts: 731
    #5
    kmygil said:

    upside down
    Arrange the glasses in a circle, upside down?

    Kirsten

    They can't be upside down in
    They can't be upside down in a circle, because then the centers will be at the corners of a square, and the ones diagonally across from each other will be further away than those at contiguous corners.
    --Greg
  • kmygil
    kmygil Member Posts: 876 Member
    #6
    PhillieG said:

    I'm missing something I guess
    with a real good ruler or you could even have them touching right side up.
    Or, if you drank all 4 glasses of wine, how would you know the difference or would it even matter?
    ;-)

    Have a great weekend!
    ;-)

    Trust you to make the best point!
    Hah! Trust you to make common sense. LOL!!!
  • PhillieG
    PhillieG Member Posts: 4,866 Member
    #7
    PGLGreg said:

    Invert 3; balance the 4th on top
    If the 4 feet are to be equidistant, they must be at the vertices of a trapezoid. To form the bottom side of the trapezoid, which is an equilateral triangle, invert 3 of the glasses on the table and place them so the sides of each touches the other two. Then balance the 4th glass upright on the bottoms of the first 3. The center of this 4th glass will be the top vertex of the trapezoid. Now raise the center of the 4th glass by inserting spacers under the bottom of this 4th glass (using coasters, perhaps), until its center is as far from the centers of the other 3 as these other 3 are from each other.
    --Greg

    Google?
    Just wondering...
  • PGLGreg
    PGLGreg Member Posts: 731
    #8
    PhillieG said:

    Google?
    Just wondering...

    Are you asking me if I found the answer I gave using Google? No, because that would be cheating. However, I did just search on "four ordinary wineglasses" and found a different answer to the puzzle that is arguably better than the one I gave. So don't stop working to find an answer. (My answer requires some auxiliary apparatus -- the coasters -- which might not be fair to assume. Someone else gave an answer not requiring coasters.)

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