IMC 2010 Q7
7. The Three Choirs Festival is held annually. Its venue rotates in a three-year cycle among Hereford, Gloucester and Worcester. In 2009, it was held in Hereford, in 2010 it will be held in Gloucester, next year it will be held in Worcester.
Assuming that this three-year cycle continues, in which one of the following years will the Festival not be held in Worcester?
- A 2020
- B 2032
- C 2047
- D 2054
- E 2077
Intermediate Mathematical Challenge 2010, Question 7. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D 2054
The Festival will next be held in Worcester in 2011. As it follows a three-year cycle, the Festival is held in Worcester when the number of the year leaves a remainder of 1 when divided by 3. So it will be held in Worcester in 2020, 2032, 2047 and 2077, but not in 2054.
Solution © UK Mathematics Trust, from the IMC 2010 solutions.