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Option B.

8 bit hash => 256 values 

On applying pigeon hole principle,

At least ceiling(k/n) pigeons on same hole...

Here , k=1000 (pigeons) & n=256 (pigeonholes) 

We get, AT LEAST 4 INPUTS WOULD BE MAPPED TO  THE SAME VALUE BY HASH FUNCTION H to each location.

In which  1000%256 = 232 values being mapped to some 232 locations (assuming they are uniformally distributed). i.e., 232 location will have minimum of 4 values and remaining 24 locations 3 values. 

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