Have You Lost Your Marbles?Discrete Mathematics Level 3
"Boys, on the table you can see 11 marbles. The two of you are going to take turns removing the marbles from the table. On your turn, you can choose to take either one, two or three marbles. Whoever ends up taking the last marble from the table will go into detention."
Since you are the Math Professors favorite student, he slyly winks at you and gives you the chance to go first.
How many marbles should you pick up from the table in your first chance to avoid detention and justify the faith your Math prof has in you?