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

Answer:

42000 seconds

Step-by-step explanation:

2^1 -1 soul become ghosts in 1 second.

2^2 -1 soul become ghosts in 2 seconds. (one merge, then ghost)

2^3 -1 soul becomes a ghost in 3 seconds. (two merges, then ghost)

Therefore, 2^42000 - 1 become ghosts in 42000 seconds.

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Answer 2

After $42000$ seconds will all souls will become ghosts

Step-by-step explanation:

Given:Total souls present on a particular day$=(2^{42000}-1)$. A single soul can merge with another soul in every second thereby reducing to a single soul and if a soul cannot merge into another soul, it will turn into ghost.

To Find:After how many seconds will all souls become ghosts.

Concept/Formula used:

Total souls present on a particular day$=2^{42000} -1$

Soul become ghosts in 1 second.$=2^1-1$

Soul become ghosts in 2 seconds. (one merge, then ghost)$=2^2-1$

soul becomes a ghost in 3 seconds. (two merges, then ghost)$=2^3-1$

Hence,$2^{42000} - 1$ become ghosts in $42000$ seconds.