Re: HSC 2015 4U Marathon - Advanced Level
It's just saying that when the n'th passenger enters, the only possible seats left will be his own or the first person's. Both cases are equally likely so it's just 1/2.
Re: HSC 2015 4U Marathon
n has to be odd, and since 2 and 3 are co-prime three consecutive odd numbers must take all possible values mod 3. This means there is exactly one of the values equal to 0 mod 3 and hence composite.
At least 2* but see below
True but they take into account other maths courses.
Say A and B both get 97 raw in 4U and are ranked 1st internally. If A gets 70 raw in 3U but B gets like 68 raw, then A ranks above B in the 4U list.