Library / UKMT Intermediate Mathematical Challenge /136 of 267

UKMT Intermediate Mathematical Challenge, 2019

Number theory Difficulty 2.0 Junior Find the answer United Kingdom

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) $24$

Figure for this problem

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.