Minor edits

Advanced/Pidgeonhole Problems/main.tex

@@ -35,7 +35,7 @@
 
 
 	\problem{}<divisibledifference>
-	You are given $n + 1$ integers. \par
+	You are given $n + 1$ distinct integers. \par
 	Prove that at least two of them have a difference divisible by $n$.
 
 	\begin{solution}
@@ -55,7 +55,7 @@
 
 
 	\problem{}
-	You have an $8 \times 8$ chess board with two opposing corner squares cut off. You also have a set of dominoes, each of which is the size of two squares. Is it possible to completely cover the the board with dominos, so that none overlap nor stick out?
+	You have an $8 \times 8$ chess board with two opposing corner squares cut off. You also have a set of dominoes, each of which is the size of two squares. Is it possible to completely cover the board with dominos, so that none overlap nor stick out?
 
 	\begin{solution}
 		A domino covers two adjacent squares. Adjacent squares have different colors. \par
@@ -253,7 +253,7 @@
 	Choose $n + 1$ integers between $1$ and $2n$. Show that you must select two numbers $a$ and $b$ such that $a$ divides $b$.
 
 	\begin{solution}
-		Split the the set $\{1, ..., 2n\}$ into classes defined by each integer's greatest odd divisor. There will be $n$ classes since there are $\frac{k}{2}$ odd numbers between $1$ and $n$. Because we pick $n + 1$ numbers, at least two will come from the same class---they will be divisible. \par
+		Split the set $\{1, ..., 2n\}$ into classes defined by each integer's greatest odd divisor. There will be $n$ classes since there are $\frac{k}{2}$ odd numbers between $1$ and $n$. Because we pick $n + 1$ numbers, at least two will come from the same class---they will be divisible. \par
 
 		For example, if $n = 5$, our classes are
 		\begin{itemize}