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Thread: I know the answer, but I cannot determine the formula

  1. #1
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    I know the answer, but I cannot determine the formula

    This is not homework. It's for a video game. But it is beyond my ability to figure it out.

    Using some or all of these numbers, can you arrive at a consistent formula that produces N for each row? You must use X and Y, all other values (including row number) are optional. You may not use zero. Any mathematical operation is allowable. You may introduce a constant not in this list.
    X Y N
    Row # Resilience Attacks Per Second Attack Duration Attack Range Power Special Power activeAbilityDelay activeAbilityBusyDuration activeAbilityCost activeAbilityRange Reported Strength
    1 5500 0.67 1 70 517 520 1.5 1 1 90 8
    2 6534 0.67 1 70 614 617 1.5 1 1 90 12
    3 7854 0.67 1 70 782 786 1.5 1 1 90 18
    4 9419 0.67 1 70 1082 1088 1.5 1 1 90 32
    5 10979 0.67 1 70 1498 1505 1.5 1 1 90 50
    6 13072 0.67 1 70 2036 2047 1.5 1 1 90 84
    7 15525 0.67 1 70 2766 2779 1.5 1 1 90 140
    8 18339 0.67 1 70 3742 3761 1.5 1 1 90 224
    9 21549 0.67 1 70 5043 5068 1.5 1 1 90 342
    10 25191 0.67 1 70 6517 6550 1.5 1 1 90 520
    11 28826 0.67 1 70 7334 7371 1.5 1 1 90 660
    12 32316 0.67 1 70 8221 8263 1.5 1 1 90 840
    13 36083 0.67 1 70 9178 9224 1.5 1 1 90 1040
    14 40169 0.67 1 70 10216 10267 1.5 1 1 90 1288
    15 44718 0.67 1 70 11372 11429 1.5 1 1 90 1590
    16 52525 0.67 1 70 13354 13420 1.5 1 1 90 2211
    17 61695 0.67 1 70 15683 15762 1.5 1 1 90 3060
    18 72467 0.67 1 70 18421 18513 1.5 1 1 90 4212
    19 85121 0.67 1 70 21636 21744 1.5 1 1 90 5796
    20 99983 0.67 1 70 25412 25539 1.5 1 1 90 8010
    21 117442 0.67 1 70 29847 29996 1.5 1 1 90 11040
    22 137949 0.67 1 70 35056 35232 1.5 1 1 90 15249
    23 162037 0.67 1 70 41175 41381 1.5 1 1 90 21006
    24 190332 0.67 1 70 48363 48605 1.5 1 1 90 29013
    25 223569 0.67 1 70 56806 57090 1.5 1 1 90 40020

  2. #2
    Elite Member stapel's Avatar
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    Cool

    Quote Originally Posted by pgneedscash View Post
    This is not homework. It's for a video game. But it is beyond my ability to figure it out.



    Using some or all of these numbers, can you arrive at a consistent formula that produces N for each row? You must use X and Y, all other values (including row number) are optional. You may not use zero. Any mathematical operation is allowable. You may introduce a constant not in this list.

    X Y N
    Row # Resilience Power Special
    Power
    Reported
    Strength
    1 5500 517 520 8
    2 6534 614 617 12
    3 7854 782 786 18
    4 9419 1082 1088 32
    5 10979 1498 1505 50
    6 13072 2036 2047 84
    7 15525 2766 2779 140
    8 18339 3742 3761 224
    9 21549 5043 5068 342
    10 25191 6517 6550 520
    11 28826 7334 7371 660
    12 32316 8221 8263 840
    13 36083 9178 9224 1040
    14 40169 10216 10267 1288
    15 44718 11372 11429 1590
    16 52525 13354 13420 2211
    17 61695 15683 15762 3060
    18 72467 18421 18513 4212
    19 85121 21636 21744 5796
    20 99983 25412 25539 8010
    21 117442 29847 29996 11040
    22 137949 35056 35232 15249
    23 162037 41175 41381 21006
    24 190332 48363 48605 29013
    25 223569 56806 57090 40020
    You say that this is not homework, but the instructions read like some kind of assignment. Is this for a programming class or something?

    The information in seven of the columns never changes, making these values irrelevant, so I've deleted those columns in the above. Is the row-number information important, or is it being used merely as a way of naming the various data points?

    What techniques have you studied recently? How to you believe you're expected to approach this project? What tools do you have?

    When you reply, please include a clear listing of your thoughts and efforts so far. While it may not be possible to backwards-engineer "the" formula that generated these data points, we may be able to help you figure out "a" formula. So please do be complete. Thank you!

  3. #3
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    Quote Originally Posted by stapel View Post
    You say that this is not homework, but the instructions read like some kind of assignment. Is this for a programming class or something?

    The information in seven of the columns never changes, making these values irrelevant, so I've deleted those columns in the above. Is the row-number information important, or is it being used merely as a way of naming the various data points?

    What techniques have you studied recently? How to you believe you're expected to approach this project? What tools do you have?

    When you reply, please include a clear listing of your thoughts and efforts so far. While it may not be possible to backwards-engineer "the" formula that generated these data points, we may be able to help you figure out "a" formula. So please do be complete. Thank you!

    I got a response! That's cool. I thought it possible that getting "the" formula might not be possible, especially since I have no idea what it is, and it could be some kind of non-reversible function.

    The instructions provided were my own, based on what I have seen and tried. If they sounded assignment-like, I was a college professor in another life, but for writing, not programming.

    It is not for a class, certification, or anything else that would require that I do it on my own. Knowing a working answer in this case provides me only with a tool I can use to publically prove a point in this game's forums--and I will definitely give credit where it is due, if that is what you wish. I can be general, specific, or say nothing at all regarding any assistance. That is the call of whomever helps me. I am not trying to steal credit for something I did not (and cannot) do. I have already admitted this is beyond me in math, but it is beyond me in programming as well.

    Thank you for cleaning up the unnecessary data. I wanted to give what I had, since I wasn't sure what might be relevant.

    As for your other questions, there is no expectation on how to solve. My guess is the game developer would prefer than I not find a solution. It's not against the TOS for me to do so, but it could negatively impact their reputation among players if the developer has been misrepresenting things to players. I have reason to believe they are doing just this, but I am having trouble proving it in a way not easily refuted. I chose this game element because it is one of the original and also does not appear to deviate from any patterns.

    Techniques studied? None recently. I took Calc I-III in college, but I'm sure I remember almost none of that, since I haven't used it. I have never taken a programming class.

    Based on what I have seen from this file about this game element and other equivalent files for other elements, the columns I have named resilience and Power must be factors. Any element that has a 0 for either value has a Reported Strength of 0. For most game elements, these two columns increase with every new row. The rows correspond to levels. I do not think the level number is part of the answer--I included it because I didn't want to leave out something simple that maybe would make a difference.

    For tools, I do not have anything fancy. I've have tried most of my attempts at a solution in Excel, both because I am familiar with it and because the original data is in a CSV format.

    I included only the first 25 rows because these are the original 25 levels, but also because I exceeded the length when I included more rows. If additional rows would help, I can include on the columns you have and add the remaining levels. They have added levels in increments of 5. And while the power and strength follow consistent increases within each set of 5, if you graph the whole development, these does not appear to be anything consistent to me.

    I hope this helps. I am not being obtuse intentionally. If I did not answer your questions, please let me know. I will try again.

    Thank you for any help you can provide, even if it isn't an answer. I greatly appreciate any assistance or nudges in what you believe to be the right direction.

  4. #4
    Elite Member stapel's Avatar
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    Cool

    You have data points, and want to backwards-engineer "the" formula. Given twenty-five data points and three input values / variables, it might be possible to obtain a regression, but this will be only one of many solutions, given the small amount of data.

    On what basis had you concluded that one could obtain "the" formula from the posted information?

    Note: The volunteers here give of their time to help struggling math students with concepts and homework exercises. It is possible that none of the volunteers will find time for this, possibly-unanswerable, question.

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