Question 1178908
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(a)  The solution is VERY SIMPLE.


     Under given condition, the numbers are  integers from  1000  to  1999, inclusive.


     In all, there are exactly 1000  (one thousand) of such numbers.



(b)  As the problem is posed, it is unclear to me, what restrictions work in this case.


    If you mean odd integer numbers of the category (a), then their amount is half of the 1000 numbers of the category (a), i.e. 500.


    If you mean all odd four-digit numbers, then the amount of such numbers is  {{{9000/2}}} = 4500.
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Solved and answered.