IMC 2008 Q23
23. Beatrix has a 24-hour digital clock on a glass table-top next to her desk. When she looked at the clock at 13:08, she noticed that the reflected display also read 13:08, as shown.
How many times in a 24-hour period do the display and its reflection give the same time?
- A 12
- B 36
- C 48
- D 72
- E 96
Intermediate Mathematical Challenge 2008, Question 23. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E 96
The only digits which will appear the same when reflected in the glass table-top are 0, 1, 3 and 8. So it is necessary to find the number of times in a 24-hour period that the display on the clock is made up only of some or all of these four digits. The first of the digits, therefore, may be 0 or 1; the second digit may be 0, 1, 3 or 8; the third digit may be 0, 1 or 3; the fourth digit may be 0, 1, 3 or 8.
So the required number is 2 × 4 × 3 × 4 = 96.
Solution © UK Mathematics Trust, from the IMC 2008 solutions.