You have a magic coin.

The first time you flip the coin it will land heads up.

The second time you flip the coin it will land tails up.

Every time you
flip the coin after that, the probability that the coin will land heads up is proportional to the number of "heads up" that "run".

So for example, the probability of the third toss landing heads up is 1/2.

If the third toss is heads, then the probability of the fourth toss landing heads is 2/3, otherwise the probability of landing heads is only 1/3.

And so on.

Find the probability that the coin will land "heads up" exactly 42 times
in the first 100 tosses (in a single run).

Source: NCH contest