IMC 2015 Q23
23. There are 120 different ways of arranging the letters, U, K, M, I and C. All of these arrangements are listed in dictionary order, starting with CIKMU. Which position in the list does UKIMC occupy?
- A 110th
- B 112th
- C 114th
- D 116th
- E 118th
Intermediate Mathematical Challenge 2015, Question 23. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B 112th
The permutations which follow UKIMC in dictionary order are UKMCI, UKMIC, UMCIK, UMCKI, UMICK, UMIKC, UMKCI, UMKIC. There are eight of these, so UKIMC is 112th in the list.
Solution © UK Mathematics Trust, from the IMC 2015 solutions. Longer versions with investigations: Solutions and investigations (PDF).