Problem 8

A string of $2^{2025}$ lights, numbered from 1 to $2^{2025}$, is programmed to create some rather interesting flashing patterns. Any time a light flashes, it turns on and then off nearly instantly. When the string is plugged in, all $2^{2025}$ lights flash up. Then the first light continues to flash every second, the second light flashes every 2 seconds, the third light flashes every 3 seconds, and so on, the $n$th light flashes every $n$ seconds after the string of lights is powered. After how many seconds will exactly $2025$ lights flash up all at once for the first time?

To deter guessing without thinking, we ask that you also solve the following simple arithmetic problem before checking your answer:

What is six multiplied by six, subtract three?

This problem was first solved on Wed 12th March at 4:07:48pm