Quiz for Doron Zeilberger’s Lecture at Math Leagues Camp, TCNJ, July 23, 2018, 1:30-2:20pm NAME: (print!) E-MAIL ADDRESS: (print!)

1. China played Soccer against Japan, and the score was China: 5; Japan:4 . How many possible game histories are there?

2. Out of these game-histories , how many were boring? How many exciting ones?

3. What ‘bad’ walk in the Manhattan lattice from (1, 0) to (5, 4) corresponds to the following walk from (0, 1) to (5, 4) ?

(0, 1) → (0, 2) → (1, 2) → (2, 2) → (3, 2) → (3, 3) → (4, 3) → (5, 3) → (5, 4)

4. What is the unique cyclic shift in the following game history between team A and team B, where team A scored 7 goals and team B scored 6 goals, that is boring.

AABBBABABAAAB ,

5. In a circular track, there are stations where the amount of gasoline (in km) is indicated in boldface, and the distances between them are written in italic.

1 3 4 4 3 3 2 6 10 4 ,

where would you start so that you will never run out of gas?