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  1. #1
    Super Dawg Member Phil Kaufman aka AffiliateHound's Avatar
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    Interesting Math
    111,111,111 x 111,111,111 = 12,345,678,987,654,321
    Since June 10, 2012 a vegan aarf but still writing the Hound Dawg Sports Blog
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  2. #2
    ABW Ambassador meadowmufn's Avatar
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    Quote Originally Posted by AffiliateHound
    111,111,111 x 111,111,111 = 12,345,678,987,654,321
    Someone has entirely too much time on their hands.
    -Don't criticize anyone til you've walked a mile in their shoes. Then when you do criticize them, you'll be a mile away and have their shoes.
    - Silence is golden. Duct Tape is silver.

  3. #3
    Super Dawg Member Phil Kaufman aka AffiliateHound's Avatar
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    Quote Originally Posted by meadowmufn
    Someone has entirely too much time on their hands.
    That would be the person who sent it to me.
    Since June 10, 2012 a vegan aarf but still writing the Hound Dawg Sports Blog
    "If you don't have time to do it right, when will you have time to do it over?" -John Wooden;
    "Raj, there’s no place for truth on the internet." -Howard Wolowitz[/SIZE]

  4. #4
    Moderator MichaelColey's Avatar
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    It's actually pretty easy to visualize how it works that way if you write out the long multiplication. A smaller example:

    Code:
       1111
     x 1111
    -------
       1111
      1111
     1111
    1111
    -------
    1234321
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  5. #5
    Newbie lody's Avatar
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    Amazing! I think it doesn't need a calculator?

  6. #6
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    It's actually pretty easy to visualize how it works that way if you write out the long multiplication

  7. #7
    More Cheesier Than Ever Cheesehead's Avatar
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    Nice! How about this one: You can cover a 64 square checker board with 32 dominoes. Each domino takes up 2 squares. However, if you remove the top left and bottom right squares from the board, it is impossible to cover the 62 squares left with 31 dominoes. Why?

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  8. #8
    Super Dawg Member Phil Kaufman aka AffiliateHound's Avatar
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    Quote Originally Posted by Cheesehead
    Nice! How about this one: You can cover a 64 square checker board with 32 dominoes. Each domino takes up 2 squares. However, if you remove the top left and bottom right squares from the board, it is impossible to cover the 62 squares left with 31 dominoes. Why?

    No matter where you start, after 30 dominoes, the last two open squares do not touch.
    Since June 10, 2012 a vegan aarf but still writing the Hound Dawg Sports Blog
    "If you don't have time to do it right, when will you have time to do it over?" -John Wooden;
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  9. #9
    More Cheesier Than Ever Cheesehead's Avatar
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    Quote Originally Posted by AffiliateHound
    No matter where you start, after 30 dominoes, the last two open squares do not touch.
    Can you prove that for every single combination of 31 dominoes? One way to do this would be by "exhaustion", listing every single possibility for the first 30 dominoes. There would be 62 places for one leftover spot and 61 places for the other, resulting in 3782 ways, not including all the ways to place the 30.

    There is a fairly simple proof for this however. You seem to be very close to getting it, based on your statement that "the last two squares do not touch".
    This World is Not My Home
    We're gonna go inside, we're gonna go outside, inside and outside. . . And then we're gonna go go go and we're not gonna stop til we get across that goalline! Quotes from the movie Rudy, 1993

  10. #10
    Moderator MichaelColey's Avatar
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    Every domino will cover both a black square and a red square. Because two red squares are removed (leaving just 30), it's impossible to put more than 30 dominos on the board.
    Michael Coley
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  11. #11
    More Cheesier Than Ever Cheesehead's Avatar
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    Quote Originally Posted by MichaelColey
    Every domino will cover both a black square and a red square. Because two red squares are removed (leaving just 30), it's impossible to put more than 30 dominos on the board.
    Yes, that is it!!
    This World is Not My Home
    We're gonna go inside, we're gonna go outside, inside and outside. . . And then we're gonna go go go and we're not gonna stop til we get across that goalline! Quotes from the movie Rudy, 1993

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