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Math Help - Number sequence driving me crazy!

  1. #1
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    Number sequence driving me crazy!

    Hello,
    I have a sequence of 99 numbers, which I cant determine the pattern for. Are you able to work it out? The numbers are actually the experience points required for a certain level in a computer game. I have been given the numbers to reach level 99 but I need to work out the XP required for the levels up to 200.

    Can anyone work out the formula please?

    The numbers are:


    Quote:
    1 10
    2 22
    3 38
    4 61
    5 95
    6 147
    7 227
    8 349
    9 499
    10 667
    11 846
    12 1032
    13 1225
    14 1425
    15 1632
    16 1846
    17 2067
    18 2295
    19 2531
    20 2775
    21 3027
    22 3287
    23 3555
    24 3831
    25 4115
    26 4407
    27 4707
    28 5015
    29 5332
    30 5658
    31 5993
    32 6337
    33 6690
    34 7052
    35 7423
    36 7803
    37 8192
    38 8590
    39 8998
    40 9416
    41 9844
    42 10282
    43 10730
    44 11188
    45 11656
    46 12134
    47 12622
    48 13120
    49 13631
    50 14155
    51 14692
    52 15242
    53 15805
    54 16381
    55 16970
    56 17572
    57 18187
    58 18815
    59 19456
    60 20110
    61 20777
    62 21457
    63 22150
    64 22856
    65 23575
    66 24307
    67 25052
    68 25810
    69 26581
    70 27365
    71 28162
    72 28972
    73 29795
    74 30631
    75 31480
    76 32342
    77 33217
    78 34105
    79 35006
    80 35920
    81 36847
    82 37787
    83 38740
    84 39706
    85 40685
    86 41677
    87 42682
    88 43700
    89 44731
    90 45775
    91 46832
    92 47902
    93 48985
    94 50081
    95 51190
    96 52312
    97 53447
    98 54595
    99 55762
    Many thanks!
    TB.
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by TomBowyer View Post
    Hello,
    I have a sequence of 99 numbers, which I cant determine the pattern for. Are you able to work it out? The numbers are actually the experience points required for a certain level in a computer game. I have been given the numbers to reach level 99 but I need to work out the XP required for the levels up to 200.

    Can anyone work out the formula please?

    The numbers are:


    Quote:
    1 10
    2 22
    3 38
    4 61
    5 95
    6 147
    7 227
    8 349
    9 499
    10 667
    Many thanks!
    TB.
    I did a quick cubic regression analysis on the first 15 elements and came up with

    y=-.2232x^3+14.9565x^2-70.5702x+94.1392

    with a correlation coefficient (R^2) of .9988.

    I don't know if that's helpful at all.
    Last edited by masters; September 22nd 2009 at 10:10 AM. Reason: Error in leading coefficient. Left off decimal point.
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  3. #3
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    Hi Masters,
    Firstly, thankyou for taking the time to help.

    Secondly, im afraid I am not very good at math (GCSE was good, but that was a loooong time ago).

    Can anyone explain how I would put your formular to practical use in my application of solving the number sequence?

    Edit: Is Y the "experience points", x the level (1 to 99)?

    Thankyou,
    Tom.
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  4. #4
    A riddle wrapped in an enigma
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    Quote Originally Posted by TomBowyer View Post
    Hi Masters,
    Firstly, thankyou for taking the time to help.

    Secondly, im afraid I am not very good at math (GCSE was good, but that was a loooong time ago).

    Can anyone explain how I would put your formular to practical use in my application of solving the number sequence?

    Edit: Is Y the "experience points", x the level (1 to 99)? Yes

    Thankyou,
    Tom.
    There was an error in my initial function. The coefficient of x^3 should be -.2232. I have edited it so it is now correct.

    However, this function does not work for large values of x because the function is cubic has a max value around x=42. If you test x=16, you get 1879 which is close to your value, but not exact.

    At 17, y=2120
    At 18, y=2367
    At 19, y=2621
    At 20, y=2879

    Bottom line, This doesn't work for you. You'll have to keep looking.
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  5. #5
    Super Member
    Joined
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    Quote Originally Posted by TomBowyer View Post
    Hello,
    I have a sequence of 99 numbers, which I cant determine the pattern for. Are you able to work it out? The numbers are actually the experience points required for a certain level in a computer game. I have been given the numbers to reach level 99 but I need to work out the XP required for the levels up to 200.

    Can anyone work out the formula please?

    The numbers are:


    Quote:
    1 10
    2 22
    3 38
    4 61
    5 95
    6 147
    7 227
    8 349
    9 499
    10 667
    11 846
    12 1032
    13 1225
    14 1425
    15 1632
    16 1846
    17 2067
    ...
    96 52312
    97 53447
    98 54595
    99 55762
    The numbers are not uniformly spread. It appears as if they are generated with separate functions:

    1 thru 11

    12 -- 18

    19 -- 28

    29 -- 38

    39 -- 48

    49 -- 98

    99 -- 198
    from 99 to 198 it appears as if this should work.

    Starting at 99.
    Whatever level you are looking for, LEVEL is the number, and the POINTS will be the result.

    k = LEVEL - 99

    Subtract 99 from the level with which you are working.


     POINTS = 9.5 k^2 + 1176.5 k + 55762

    Hope that helps.
    There is not enough data to guess the next incrementing step beyond level 198.

    .
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