Two neighbours carpool into work, driving alternately in strict rotation. They work exactly the same days as each other - Monday to Friday each week and every other Saturday. What is the maximum number of days each must drive in a calendar month?

Multiple choice answers - 11, 12, 13, 14, 15
If they worked every day of the longest month(31 days), the maximum would still only be 16 days. To drive 15 days, they would need to work for 30/31 days, so we know from the start that 15 is unrealistic.
If we imagine that on the first week, the two people work on the Saturday(in fact it doesn't matter whether we imagine they work Saturdays on odd or even weeks). In the first week, they work 6 days and so each drives 3 days.
In week 2, they work 5 days so one of the neighbours(who drove on the Monday of week 1) drives 3 days, while the other drives 2 days.
On week 3, they work 6 days and so each will drive for 3 days. The one who drove for 3 days in week two will drive on Saturday of week 3 and therefore will only drive for 2 days of week 4 while the other neighbour drives for 3 days.
At the end of week 4, each neighbour has driven for 11 days. There are 3 days left of week 5(Monday-Wednesday). The neighbour who drove on Monday of week 1, will drive on Monday of week 5 and Tuesday of week 5. Thus, the neighbour who drives the most will be the one who drives on Monday of week 1 and they will drive for 13 days at most.