After winning the challenge fair and square, and winning a Snorlax, Max finally reaches Viridian City. As he enters viridian city, he notices that there is a Pokémon trainer in front of the gym. I will only let you pass if you beat me in my favourite game, he says. This is a game played with a sequence of tiles, each labelled with two numbers. You start at the first the 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. 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. Now, you are given the following tiles. What is the maximum score you can make to ensure you beat the security guard?
