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Math Help - Middle day in a year

  1. #1
    Senior Member DivideBy0's Avatar
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    Middle day in a year

    The middle date of the year in 2006 is:

    (a) 29th June
    (b) 30th June
    (c) 1st July
    (d) 2nd July
    (e) 3rd July

    We are meant to assume that 2006 is not a leap year. The problem came when I tried \frac{365}{2} and didn't get an integer...
    My answer so far is 2nd July....
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by DivideBy0 View Post
    The middle date of the year in 2006 is:

    (a) 29th June
    (b) 30th June
    (c) 1st July
    (d) 2nd July
    (e) 3rd July

    We are meant to assume that 2006 is not a leap year. The problem came when I tried \frac{365}{2} and didn't get an integer...
    My answer so far is 2nd July....
    I'm going to use a much smaller "year" as a demonstration here.

    Think of it this way, say the year has 9 days in it. What is the middle day of the year?

    Well, we have days
    1 2 3 4 5 6 7 8 9
    By inspection it looks like the middle day is 5. But 5 \neq \frac{9}{2}. So how do we approach this?

    Well, what you did amounts to solving 2n= 365, which gives a noninteger day. The reason for this is that 365 isn't even. But even then the middle day of an even list has no middle! For example
    1 2 3 4 5 6 7 8
    What is the middle number? There isn't one!

    What this amounts to is that it is better to solve the equation 2n - 1 = 365. This will give you the correct day number. You can easily verify that this gives you the correct solution when the list has 9 elements.

    -Dan
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