Problem 1. Anya calls a date beautiful if all 6 digits of its notation are different. For example, 19.04.23 is a beautiful date, while 19.02.23 and 01.06.23 are not.

a) How many beautiful dates will there be in April 2023?

b) How many beautiful dates are there in total in 2023?
Answer. a) 5; b) 30.

Solution. a) Note that in April, the date is written as **.04.23. Therefore, the first two digits can only be $1,5,6,7,8,9$. Of these digits, only 1 can be the first, so there are five dates in total: $15,16,17,18,19$ April.

b) See the solution to problem 1 for 7th grade (p. 9).