Algebra

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Snap to It...
I snap my fingers now, in one second, I smap them again. I wait two seconds and snap them a third time. I wait 4 seconds before snapping them again. Then I wait eight, then sixteen, and the pattern continues. The interval between each snap doubles each time. How many times will I snap my fingers during the next year.

  • Algebra -

    so you are really asking ...

    1+2+4+8+16 + .... = number of seconds in a year
    left side is the sum of a GS with
    a = 1, r = 2
    seconds in a year = 365(24)(60)960) = 31536000

    sum(n) of GS = a(r^n - 1)/(r-1)
    = a(2^r -1)/1

    2^r - 1 = 31536000
    2^r = 31536001
    r log2 = log 31536001
    r = 24.9

    by the time you snap 25 times, the year would be over, so you can only snap 24 times

    check:
    24 snaps --- > 24 terms of 1+2+4+ ..
    = 1(2^24 - 1)/(2-1)2 = 16777215 < less than seconds in a year

    25 snaps ---> 25 terms of 1+2+4+...
    = 2^25 -1 = 33554431 > seconds in a year

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