How to solve the 4-class problem?

Question

Mathematics

I accidentally came across an all-Russian problem book for the 4th grade of an ordinary school ...

The electronic clock shows hours and minutes (from 00:00 to 23:59). How many times per day do only the numbers 2 and 5 or one of these numbers participate in the set of numbers on the scoreboard of this watch?

Basically not interested in the answer. The logical course of the solution is interesting ... Or rather, the search for an elegant beautiful solution ...

Answer 1

Ordinary combinatorics.
For minutes, there are 4 valid combinations: 22, 25, 52, 55. For hours, there is 1 valid combination: 22.
Multiply 4 and 1, we get 4 combinations (22:22, 22:25, 22:52, 22:55).

Answer 2

In the 4th grade, this problem is elegantly solved by brute-force search.

Answer 3

Actually overkill. Write down which of the numbers can be in each position
ab:cd
a={0,1,2}
b={0,...,9}
c={0,...,5}
d={0,.. .9}
then consider each case:
only the number 5 is involved - it disappears, since 5 ∉ a
and so on, only in simpler words.

Answer 4

Answer: 4
22:25, 22:52, 22:55
22:22
Keywords:

only _ _