What is the largest n for which one can solve within one second a problem using an algorithm that requires f(n) bit operations, where each bit operation is carried out in 10−9 seconds, with these functions f(n)?

For questions (a) to (c), enter the exact answers. Enter brackets around compound exponents. For example, abc should be entered as a^(b^c). Round your answers down to the nearest integer for all other parts. Note that logn=log2n.

n! n=

Question

What is the largest n for which one can solve within one second a problem using an algorithm that requires f(n) bit operations, where each bit operation is carried out in 10−9 seconds, with these functions f(n)?

For questions (a) to (c), enter the exact answers. Enter brackets around compound exponents. For example, abc should be entered as a^(b^c). Round your answers down to the nearest integer for all other parts. Note that logn=log2n.

n!  n=