BEBRAS 2025 Grade 11-12 Round 2 Ext Question 10

Cards form strings of A,B,C. You may cover letters using the supplied spare cards to maximize the score. Each consecutive group of two identical letters scores 2, three scores 3, and similarly for longer groups. Each letter is counted in at most one group; isolated letters score 0. The example BCACB initially scores 0 and has spare cards A,B.



Cover the first C by A and the second C by B to obtain BAABB, scoring 2+2=4.



Here is the target row and its three spare cards.



What is the greatest attainable score?