PK 2016 Q7
7. Angelo wrote down the word TEAM. He then swapped two adjacent letters around and wrote down the new order of the letters. He proceeded in this way until he obtained the word MATE. What is the least number of swaps that Angelo could have used?
- A 3
- B 4
- C 5
- D 6
- E 7
Pink Kangaroo 2016, Question 7. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C 5
In order to get from TEAM to MATE, at some point M will have to pass each of T, E and A. Likewise Angelo will have to move A in front of T and E. So at least 5 swaps are required. The list: TEAM, TEMA, TMEA, MTEA, MTAE, MATE shows it can be done in five swaps.
Solution © UK Mathematics Trust, from the PK 2016 solutions.