The query q and denominator q being the same letter is really confusing !!

Why is this in the easy section? lol

I managed to solve the problem on the Project Euler webpage. However my solution are decimals like: 0.33333333333 for the example given here (with 1 as input). How is it possible to recover the rational expression (fraction of integer a/b) from my result to then express it in the weird modulo formulation as asked in the problem statement? I'm confused

Maybe I'm a fool but I am completely lost on how the answer is 1/3.

I wanted to ask how people are handling player two's decision as to how many coins to toss when n > 1. It seems that regardless of how many coins are used, the expected value of the result is the same since the points gained doubles with each additional coin and the probability of success is halved.

T | Probability | Score | E.V.

1 | 1/2 | 1 | 1/2

2 | 1/4 | 2 | 1/2

3 | 1/8 | 4 | 1/2

4 | 1/16 | 8 | 1/2

Should Player 2 use as many coins as possible to reach n in less turns or should P2 use 1 coin each time to maximize the chance of scoring any points? Or is the decision inconsequential as all decisions result in the same E.V?