The entries in a certain row of Pascal's triangle are \[1, n, \dots, n, 1.\] The average of the entries in this row is $4/3$. Find $n$.
The sum of any row of entries = 2^n , where n = 0,1,2,3........
So the average = 2^n / ( n + 1) where n = 0,1,2,3.....
So
2^n / ( n + 1) = 4/3
Note that this is true when n = 2
+1678 
