Question

A single soul can merge with another soul in every second, and thus two souls get reduced to a single soul. If a soul cannot merge with another soul, then it becomes a ghost. Every soul tries not to become a ghost. On a particular day, there were (2^42000 - 1) souls. After how many seconds will all souls become ghosts​

Answer 1

42,000 seconds

To merge together, 2 souls are required. Which means every second two souls merge as one. The number of souls are (2^42000 -1) meaning at a certain time there are an odd number of souls.

This assumption as 2 to any exponential always returns an even number and the difference between even and odd number is always an odd number.

Let us assume that one soul that needs to be removed to form an even number does not get a soul to pair with. Thus. every second the number of souls will be halved.

Meaning, $\frac{2 ^ (42000)}{2}$ = 2^41999

Thus, it will take 41999 seconds for all of these souls to merge as one which will leave just one soul along with the odd one we left out at the beginning. These two souls will merge as well leaving a single soul to become a ghost which will amount for the 42000th second.

Thus, it will take 42000 seconds for all souls to become ghosts.