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- Jan 29, 2012

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Mathematicians often have trouble with simple arithmetic!There are integer part of 999/2= 499 even numbers les than or equal to 999. There are integer part of 999/7= 142 multiples of 7 less than or equal to 999. But 499+ 142= 1141 is too larger because it counts multiples of 14 twice. We need to subtract integer part of 999/14= 71 to account for that.

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- Mar 1, 2012

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2(1), 2(2), 2(3), ... , 2(499)

multiples of 7 less than 999 ...

7(1), 7(2), 7(3), ... , 7(142)

multiples of 14 less than 999 which are common to both lists above ...

14(1), 14(2), 14(3), ... , 14(71)

number of multiples of 2 or 7 that are less than 999 =

(multiples of 2)+(multiples of 7)-(number of values that are multiples of both 2 and 7) =

499+142-71

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