IMC 2019 Q4
4. A 24-hour digital clock shows the time in hours and minutes.
How many times in one day will it display all four digits 2, 0, 1 and 9 in some order?
- A 6
- B 10
- C 12
- D 18
- E 24
Intermediate Mathematical Challenge 2019, Question 4. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B 10
In order from 00:00, the times when the digits 2, 0, 1, 9 appear in some order are 01:29, 02:19, 09:12, 09:21, 10:29, 12:09, 19:02, 19:20, 20:19 and 21:09. So, in total, there are ten such times.
Solution © UK Mathematics Trust, from the IMC 2019 solutions. Longer versions with investigations: Solutions and investigations (PDF).