If we could have 0 come first, and we didn't care 
whether they were even or odd, there would be these 100:

00, 01, 02, 03, ..., 08, 09, 10, 11, ..., 98, 99

We take away these 10, which are really 1-digit numbers: 

00, 01, 02, 03, ..., 08, 09

and that leaves these 90:

10, 11, ..., 98, 99

half of those 90 are even and the other half odd, and
since half of 90 is 45, we have these 45

10, 12, ..., 96, 98

So 45 is the answer to (a)

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Now if we take away these 4 with repetition:

22, 44, 66, 88

then we have only 41

So 41 is the answer to (b)

Edwin