KVPY 2013 - 2

Let $n$ be a positive integer such that $\large \log_2\log_2\log_2\log_2\log_2(n)<0<\log_2\log_2\log_2\log_2(n)$

Let $l$ be the number of digits in the binary expansion of $n$ .

Then the minimum and maximum possible values of $l$ are

Try the whole set KVPY 2013 SB/SX here.