Jenny's grandmother has $24$ cats.  Seventeen of the cats do not catch mice.  Ten of the cats have black fur.  What is the smallest possible number of cats that do not catch mice that have black fur?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Jenny's grandmother has $24$ cats.  Seventeen of the cats do not catch mice.  Ten of the cats have black fur.  What is the smallest possible number of cats that do not catch mice that have black fur?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
3
Jenny's grandmother has $24$ cats.  Seventeen of the cats do not catch mice.  Ten of the cats have black fur.  What is the smallest possible number of cats that do not catch mice that have black fur?
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