It’s time for one of the most awaited events of the Tri-Wizard Tournament, The Yule Ball. Viktor Krum decides to ask out Hermione as his date for the ball. Knowing how smart she is, he decides to impress Hermione by scoring the highest ever score in one the most played games at Hogwarts The game is described as follows: This is a game played with a sequence of tiles, each labelled with two numbers. You start at the first tile in the sequence and choose one number from each tile that you stop at, according to the following rules:
• At tile i, if you pick up the smaller number, you move on to the next tile, i+1, in the sequence.
• At tile i, if you pick up the larger number, you skip the next tile and move to tile i+2 in the sequence.
The game ends when your next move takes you beyond the end of the sequence. Your score is the sum of all the numbers you have picked up. The goal is to maximize the final score. For example, suppose you have a sequence of four tiles as follows: Then, the maximum score you can achieve is 3, by choosing the numbers that are circled.
In each of the cases (a) and (b) below, compute the maximum store that Viktor can achieve by picking up numbers according to the rules given above.
A. 14,14
B. 13,14
C. 14,15
D. 14,16
