A quiz show host asks each of four contestants up to 15 questions. This process is repeated again for a second round. The 'score' is the number of questions answered correctly. The scores after each round are announced in numerical order. After the first round of the contest the scores are 8, 10, 11 and 14.
After the second round the total scores for the contestants were 13, 18, 20 and 24.
What was the largest possible score achieved in the second round of this contest?