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Floor and ceiling problem

  1. Aug 11, 2011 #1
    For integers 'n' and 'm', find the value of ceiling[(n+m)/2] + ceiling[(n-m+1)/2].
  2. jcsd
  3. Aug 11, 2011 #2


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    Consider the two cases separately, of
    1. Either both even or both odd and
    2. One odd the other even.
  4. Aug 12, 2011 #3
    Just split it into cases.

    (1) m and n have the same parity (either both odd or both even); or
    (2) m and n have different parities (one odd and the other even).

    In both cases, you can explicitly find the ceilings in question.
  5. Sep 17, 2011 #4
    can you please tell me more in detail as to how to consider those two separately with even and odd parities
  6. Sep 17, 2011 #5


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    How can you express an even integer? Odd integer? Once you have expressions for each, go through each case and plug them in. After you do this, you can evaluate explicitly what the answer is.
  7. Sep 17, 2011 #6


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    The sum of difference of two even numbers is even, the sum or difference of two odd numbers is even. The sum or difference of one odd and one even number is even. Fit those into your formula. The crucial point is that in any case one of (n+m)/2 and (n- m+ 1)/2 is an integer and the other is a half integer.
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