GK 2018 Q14
14. A hotel on an island in the Caribbean advertises using the slogan ‘350 days of sun every year!’ According to the advert, what is the smallest number of days Will Burn has to stay at the hotel in 2018 to be certain of having two consecutive days of sun?
- A 17
- B 21
- C 31
- D 32
- E 35
Grey Kangaroo 2018, Question 14. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D 32
The slogan suggests that there will be at most 15 days without sun in 2018. In this case it is possible to have a run of 31 days without having two consecutive days of sun by alternating a sunny day with a non-sunny day, starting with a sunny day. Hence Will Burn has to stay for one further day, or 32 days in total, to be certain of having two consecutive days of sun.
Solution © UK Mathematics Trust, from the GK 2018 solutions.