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  1. #1 just for fun... 
    Moderator Moderator AlexP's Avatar
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    just for fun... See if you can determine how I came up with these numbers. There's a pattern.

    0, 1, 15, 40, 85, 156, 259, 400, 585, 820 ...


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  3. #2  
    Forum Ph.D. GhostofMaxwell's Avatar
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    Tough one(as always) as I cant find a linear recurrence relationship.
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  4. #3  
    Moderator Moderator AlexP's Avatar
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    Quote Originally Posted by GhostofMaxwell
    Tough one(as always) as I cant find a linear recurrence relationship.
    Is RiverRat here???
    There isn't one equation that governs all of the numbers. They're just related in the way they're obtained, which isn't really through an equation.
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  5. #4  
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    Come on all you smart people in this forum, don't let this fool you. I know you can do it.

    Just work on the first three values actually, then test the rest from there. It's not difficult once you get the concept, which can be obtained through the first couple numbers.
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  6. #5  
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    Ok, this is incomplete, but I'll just give it a try.

    0, 1, 15, 40, 85, 156, 259

    (1*0), ( 2* 1/2), ( 3*5), ( 4*10), (5*17), (6*26), (7*37)...

    The first number in the bracket (i.e 1,2,3,4...) indicates the position of the term in the pattern.
    As for the second number ( 0, 1/2, 5, 10, 17, 26, 37...)

    The difference between these numbers is ( 1/2, 4.5, 5, 7, 9, 11...)

    I'm not sure about the first 2 terms ( 0.5 and 4.5) but for all the next terms, they are consecutive odd numbers.
    So, excluding the first 2 terms, the numbers in the pattern are products of their position in the pattern and a number that , when having the previous one in the pattern subtracted from it, would give you consecutive odd numbers... ( I know, this is really badly explained, needless to say, probably wrong...)
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  7. #6  
    Moderator Moderator AlexP's Avatar
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    I never would've thought of anything that complicated, you're much smarter than me.
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  8. #7 just for fun 
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    0=0+0+0+0 base 0
    1=1+1+1+1 base 1
    15=8+4+2+1 base 2
    40=27+9+3+1 base 3
    85=64+16+4+1 base 4
    156=125+25+5+1 base 5
    259= 216+36+6+1 base 6
    ............
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  9. #8 Re: just for fun 
    Moderator Moderator AlexP's Avatar
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    Quote Originally Posted by zebeke
    0=0+0+0+0 base 0
    1=1+1+1+1 base 1
    15=8+4+2+1 base 2
    40=27+9+3+1 base 3
    85=64+16+4+1 base 4
    156=125+25+5+1 base 5
    259= 216+36+6+1 base 6
    ............
    Or 1111 in each base. Yep, you got it.
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  10. #9  
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    It's not totally right though.

    Base 0 is 1+0+0+0=1
    Base 1 is 1+1+1+1=4

    So the row should be
    1,4,15,40,85,156,259,400,585,820,1111,...

    :-)
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  11. #10  
    Moderator Moderator AlexP's Avatar
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    Quote Originally Posted by zebeke
    It's not totally right though.

    Base 0 is 1+0+0+0=1
    Base 1 is 1+1+1+1=4

    So the row should be
    1,4,15,40,85,156,259,400,585,820,1111,...

    :-)
    True, I didn't catch that. But actually, I also didn't catch that you can't have 1s and 0s in bases 0 and 1, because the numbers you use for one digit can only be smaller, so it doesn't matter anyway.
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  12. #11  
    Forum Professor serpicojr's Avatar
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    Lame but fun question: what's everyone's favorite base? Mine is 12. Divisible by 2, 3, 4, and 6, it's way more convenient than 10 (and will be handy if we grow some extra fingers). If we could keep track of such large numbers, base 60 would be even better, but given our mental limitations, 12 take the cake.
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  13. #12  
    The Doctor Quantime's Avatar
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    Quote Originally Posted by serpicojr
    Lame but fun question: what's everyone's favorite base? Mine is 12. Divisible by 2, 3, 4, and 6, it's way more convenient than 10 (and will be handy if we grow some extra fingers). If we could keep track of such large numbers, base 60 would be even better, but given our mental limitations, 12 take the cake.
    So why'd they abandon the imperial system?
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  14. #13  
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    Because I wasn't there to stop them.
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  15. #14  
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    or x³+x²+x+1

    0³+0²+0+1= 1
    1³+1²+1+1= 4
    2³+2²+2+1= 15
    3³+3²+3+1= 40
    4³+4²+4+1= 85
    etc....

    :wink:
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  16. #15  
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    Let D be a circular dish of radius z and depth a. What is the content of D?

    Oh dear, thats so lame, sorry folks.
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