Over winter break, Ann, Blake, and Carl are bored, so they decide to make a deck of 2019
cards numbered 1 through 2019. Each of them gets 673 of these cards, split up as follows:

Person       Card numbers

Ann            1, 2, . . . , 673

        Blake          674, 675, . . . , 1346
Carl             1347, 1348, . . . , 2019

They play a cooperative game with these cards as follows: Each player plays a card, taking turns, in the order A → B → C → A → B → C → · · · . The game ends when the sum of all the cards played is a multiple of 3. Their goal is to have the game last as long as possible. If they cooperate, how many cards will be played in the longest possible game? Explain the strategy that achieves this goal.

Barge Prizes
First Prize        $1000
Second Prize   $750
Third Prize       $500

1. Form a team with other Lafayette students. Each team must have 3, 4 or 5 members.
2. The weekly problem will be posted online https://math.lafayette.edu/teambarge/ and in the Math
   Dept. There will be 8 problems during the semester.
3. Get your solution to Gary Gordon by Friday, Feb. 15. You can either turn in a hard copy or send
   your solution by email to [email protected].
4. Don’t Quit! Keep turning in problems, even if you’re not 100% sure of your solution.

Due Date: Friday, Feb. 15.