### Instruction: Assume we have a calendrical system in which leap years happen every four years, no matter what. In a 150-year period, what is the maximum possible number of leap years?### Response: The problem is asking for the maximum number of leap years, so I want to find a way to maximize the number of multiples of four in the 150-year period.
One way to do that is to start and end the period with a leap year, so that I have two extra leap years at the edges.
For example, if I start the period with the year 2000 and end it with the year 2149, I have a 150-year period that starts and ends with a leap year.
Now I need to count how many multiples of four are in this period.
I can use a formula for the number of multiples of k in an interval [a, b]: it is (b // k) - ((a - 1) // k), where // is the integer division operator.
In this case, k = 4, a = 2000, and b = 2149, so the formula gives me (2149 // 4) - ((2000 - 1) // 4) = 537 - 499 = 38.