IMC 2014 Q5
5. A ship's bell is struck every half hour, starting with one bell at 0030, two bells (meaning the bell is struck twice) at 0100, three bells at 0130 until the cycle is complete with eight bells at 0400. The cycle then starts again with one bell at 0430, two bells at 0500 and so on. What is the total number of times the bell is struck between 0015 on one day and 0015 on the following day?
- A 24
- B 48
- C 108
- D 144
- E 216
Intermediate Mathematical Challenge 2014, Question 5. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E 216
In one complete cycle of 4 hours, the clock is struck 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36 times. So in 24 hours the clock is struck 6 × 36 = 216 times.
Solution © UK Mathematics Trust, from the IMC 2014 solutions. Longer versions with investigations: Solutions and investigations (PDF).