Yashchenko I.V.

In Mexico, ecologists have succeeded in passing a law according to which each car must not be driven at least one day a week (the owner reports to the police the car's number and the "day off" for the car). In a certain family, all adults wish to drive daily (each for their own business!). How many cars (at a minimum) should the family have if there are

a) 5 adults? b) 8 adults?
b) If no more than one car "rests" each day, then there are no more than 7 cars in total.

## Solution

a) Five cars are not enough, because on the day when one of the cars is "resting," someone will have no car to ride in. Six cars, obviously, are enough.

b) If no more than one car "rests" each day, then the total number of cars is no more than the number of days in a week, which is seven. But this is obviously not enough. Therefore, on some day, two cars are resting, and on that day, at least 8 cars are needed. In total, 10 cars are required. We have proven that it is impossible to manage with fewer than ten cars.

Ten cars are sufficient: for example, each working day, two cars rest.

## Answer

a) 6 ; b) 10 cars.