I don't think its a logic problem

Till first five balls maximum runs are 30 and then the person cannot hit a six, so had to take three runs. And then in next over 36.

Our goal is to make mximum runs, that would mean that player should be able to play the maximum number of balls available. It might seem intuitive that he can hit a six on all the 12 balls and get a total of 72. But, at the end of the first over, if the batsman takes an ever number of runs, he won't be able to play the first ball of the next over. Hence he should take the maximum number of odd runs to change the strike, which is 3 runs. Instead of the 6 we wanted to count, he will be able to get only 3 runs, which is in total 3 less than 72 = $\boxed{69}$

Maximum runs for $n$ overs, the batsman will be able to make is:

$(n-1) \times 33 + 36 = \boxed{33n + 3}$