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AMC10 2004a Test Paper
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Sample Question 24:

Let \(f\) be a function with the following properties:

(i) \(f(1) = 1\), and

(ii) \(f(2n) = n \cdot f(n)\) for any positive integer \(n\).

What is the value of \(f(2^{100})\)?

\(\mathrm{(A) \ } 1 \qquad \mathrm{(B) \ } 2^{99} \qquad \mathrm{(C) \ } 2^{100} \qquad \mathrm{(D) \ } 2^{4950} \qquad \mathrm{(E) \ } 2^{9999}\)




Answer Keys

Question 24: D