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Yet Another Pattern?

  1. May 19, 2005 #1
    I think this one is kind of tough, so if you can't get it after a bit then maybe it's too tough. What's the next line?

    1
    1 2
    1 3 2
    3 1 4 2
    1 4 2 5 3
    1 6 4 2 5 3
    3 1 2 6 4 7 5
    1 8 2 5 3 7 4 6
    3 1 4 2 9 7 5 8 6
    _ _ _ _ _ _ _ _ _ _
     
  2. jcsd
  3. May 24, 2005 #2
    What is the answer to this pattern?
     
  4. May 25, 2005 #3
    1
    1 2
    1 3 2
    3 1 4 2
    1 4 2 5 3
    1 6 4 2 5 3
    3 1 2 6 4 7 5
    1 8 2 5 3 7 4 6
    3 1 4 2 9 7 5 8 6
    6 5 8 1 2 10 3 7 4 9

    Now, for the reason why...

    As you can see you have multiple rows, and each row number tells you how many digits are in each row. Each sequencial digit from 1 to r (where r is the row number) is in that row. S your pattern (with "0" as a place holder) is like this:

    0
    0 0
    0 0 0
    0 0 0 0
    0 0 0 0 0
    0 0 0 0 0 0
    ... etc...

    So... place the first number in the sequence down:
    1
    Then, move to the next row since you're reached r.
    Next row will give it all away; but see how it works....

    Place 1, then 2; but to find out where "2" goes, you need to look at the row before it and start from the left and put it that many places over from the current number you are placing. Take this example.

    1 3 2
    3 1 4 2

    Working on that bottom row you have

    1 3 2
    0 0 0 0

    Place the 1:

    1 3 2
    1 0 0 0

    Now look at the row above. Place the "2" 1 place over since the row above starts with a 1:

    1 3 2
    1 2 0 0

    Now place the "3"... to do that, you'll notice in the row above that 3 comes after the 1, so you need to place the "3" 3 places to the right of the two (and this wraps around). So you then have:

    1 3 2
    3 1 2 0

    Now place the "4" 2 places over from the "3":

    1 3 2
    3 1 4 2

    Clear as mud? I told you it would be hard. Sorry about this one... a little too tough to be seen I guess. No real math, just a dumb pattern that's hard to see.
     
  5. May 25, 2005 #4
    [white]
    Now look at the row above. Place the "2" 1 place over since the row above starts with a 1:

    1 3 2
    1 2 0 0

    Now place the "3"... to do that, you'll notice in the row above that 3 comes after the 1, so you need to place the "3" 3 places to the right of the two (and this wraps around). So you then have:

    1 3 2
    3 1 2 0

    Now place the "4" 2 places over from the "3":

    1 3 2
    3 1 4 2

    [white]
    can you please re explain in englsih
     
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