Saturday, April 5, 2014

Math POTW #25



7 comments:

  1. Hello guys!
    So in a 10 set of dominoes, I think there should be 56 tiles.
    So to start off, I know that in a 2 set, there are 6 different tiles. If I make it a 3 set, there would be 10 tiles, 4 tiles more than the 2 set. If I made it a 4 set, it was 15, 5 more than the 3 set! So my statement would be to start on the second term with 6, add 4, and add 1 to the amount you add each time (from second to third term you add 4, from third to fourth you add 5, and so on). If I kept going like this, eventually, I would reach 56 for the tenth term.

    Although this method of answering was somewhat amateur (I couldn't find an algebraic expression to plug in >,<), this is what I believe to be the correct answer!!!

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    Replies
    1. From what I understand, you found out how many tiles are in a specific pair (e.g 3 set, 4 set...) and continued on from there? Sort of like this format:

      2 Set + 3 Set + 4 Set... = 56 ?

      Delete
    2. Yes, it was my intention to go through that method, but it was incorrect -.-
      Good job to everyone who got 66!!!!!

      Delete
  2. Hello.

    My brother and I found out that their will be 66 tiles in a 10-set of dominoes.

    For each tile their are two terms. (1st term is the left, 2nd is the right.) The rule we made was that the 2nd term can not be lower than the first. This means that the 1st and 2nd term must always be the same or at a greater amount. e.g 1,1 -> 1,2 -> 1,3 -> 1,4...1,10

    We used this rule with all the numbers (0-10)

    These numbers would take the place of the first term (so all combinations would start from 0-10)
    e.g
    0,1
    1,1
    2,2
    3,3

    Applying to all numbers, we got 66 tiles. One feature we noticed is this..:

    *FIRST NUMBER = FIRST TERM

    0 = 11 combinations
    1 = 10
    2 = 9
    3 = 8
    4 = 7
    5 = 6
    6 = 5
    7 = 4
    8 = 3
    9 = 2
    10 = 1

    We noticed that the number of combinations for a different starting term decreases by 1 each time (when it is arranged in a 0-10 format)

    To make things easier, we just added the # of combinations to identify the number of tiles

    11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 66

    Okey tank you so mat.

    - Jon and Rach

    ReplyDelete
  3. 0,0
    0,1
    0,2
    0,3
    0,4
    0,5
    0,6
    0,7
    0,8
    0,9
    0,10
    1,1
    1,2
    1,3
    1,4
    1,5
    1,6
    1,7
    1,8
    1,9
    1,10
    2,2
    2,3
    2,4
    2,5
    2,6
    2,7
    2,8
    2,9
    2,10
    3,3
    3,4
    3,5
    3,6
    3,7
    3,8
    3,9
    3,10
    4,4
    4,5
    4,6
    4,7
    4,8
    4,9
    4,10
    5,5
    5,6
    5,7
    5,8
    5,9
    5,10
    6,6
    6,7
    6,8
    6,9
    6,10
    7,7
    7,8
    7,9
    7,10
    8,8
    8,9
    8,10
    9,9
    9,10
    10,10

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  4. LET'S DO THIS!!!!!!!
    0,10 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0,0
    1,10 1,9 1,8 1,7 1,6 1,5 1,4 1,3 1,2 1,1
    NOTE THAT I DIDN'T LIST 1,0, AS IT WAS ALREADY LISTED.
    SO, THERE IS 11 IN THE FIRST LINE, 10 IN THE NEXT, AND SO ON UNTIL YOU REACH THE LAST DOMINO, 10,10. 11+10+9+8+7+6+5+4+3+2+1=66. THERE ARE 66 DOMINOES IN THE SET.

    ReplyDelete
  5. Good work. The correct answer WAS 66.
    Full sentence answers! "The total number of dominoes in a 10-set is
    1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 = 66."

    ReplyDelete