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\centerline
{
\bf  Quiz  for Doron Zeilberger's Lecture at Math Leagues Camp, TCNJ, July 23, 2018, 1:30-2:20pm
}
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{\bf NAME:} (print!) $\underline
{\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$
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{\bf E-MAIL ADDRESS:} (print!) 
$\underline
{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$
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{\bf 1.} China played Soccer against Japan, and the score was 

China: 5; \quad Japan:4 \quad . 

How many possible game histories are there?

\bigskip\bigskip\bigskip\bigskip\bigskip\bigskip \bigskip

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

\bigskip\bigskip\bigskip\bigskip\bigskip\bigskip 

{\bf 3.} What `bad' walk in the Manhattan lattice from $(1,0)$ to $(5,4)$ corresponds to the following walk from $(0,1)$ to $(5,4)$ ?

$$
(0,1) \rightarrow (0,2) \rightarrow (1,2) \rightarrow (2,2) \rightarrow (3,2) \rightarrow (3,3) \rightarrow (4,3) \rightarrow (5,3) \rightarrow (5,4)
$$

\bigskip\bigskip\bigskip\bigskip\bigskip\bigskip \bigskip\bigskip\bigskip\bigskip\bigskip\bigskip

{\bf 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.

$$
A A B B B A B A B A A A B \quad ,
$$



\bigskip

{\bf 5.} In a circular track, there are stations where the amount of gasoline (in km) is indicated in {\bf boldface},
and the distances between them are written in {\it italic}.
$$
{\bf 1} \quad {\it 3} \quad {\bf 4} \quad {\it 4} \quad {\bf 3} \quad {\it 3} \quad {\bf 2} \quad {\it 6}  \quad {\bf 10} \quad {\it 4}  \quad ,
$$
where would you start so that you will never run out of gas?


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