Question 35
In Autolândia, car plates use three-digit strings from 000 to 999. To reduce pollution, mayor Pietro introduces driving restrictions specifying the days on which cars may be used:
- Monday: only odd plate numbers.
- Tuesday: only plates with digit sum at least 11.
- Wednesday: only plate numbers divisible by 3.
- Thursday: only plates with digit sum at most 14.
- Friday: only plates containing at least two equal digits.
- Saturday: only plate numbers strictly less than 500.
- Sunday: only plates with all three digits at most 5.
a) On which days can the car with plate 729 travel?
b) Maria, the mayor's wife, wants a car that can travel every day except Sunday. What plate should she have?
c) Mayor Pietro needs a plate allowing him to travel every day. What plate should he have?
d) Why can every resident of Autolândia travel at least once per week?
- Monday: only odd plate numbers.
- Tuesday: only plates with digit sum at least 11.
- Wednesday: only plate numbers divisible by 3.
- Thursday: only plates with digit sum at most 14.
- Friday: only plates containing at least two equal digits.
- Saturday: only plate numbers strictly less than 500.
- Sunday: only plates with all three digits at most 5.
a) On which days can the car with plate 729 travel?
b) Maria, the mayor's wife, wants a car that can travel every day except Sunday. What plate should she have?
c) Mayor Pietro needs a plate allowing him to travel every day. What plate should he have?
d) Why can every resident of Autolândia travel at least once per week?