+1800 The entries in a certain row of Pascal's triangle are
1,n,…,n,1.
The average of the entries in this row is 2. Find n.
+1633 The entries in row n of Pascal's triangle are 1, n,..., n, 1. Additionally, the sum of row n's elements is 2^n.
Additionally, row n has n + 1 terms, so we know from the problem that 2nn+1=2.
Cross multiplying, you get 2n=2n+2. The question here is trivial by bash => you will find that n = 3 works. (If you are a quick guess + checker, you might've found that right of the bat quickly, as row 3 is 1, 3, 3, 1 which has an average entry of 2.)
+1633 The entries in row n of Pascal's triangle are 1, n,..., n, 1. Additionally, the sum of row n's elements is 2^n.
Additionally, row n has n + 1 terms, so we know from the problem that 2nn+1=2.
Cross multiplying, you get 2n=2n+2. The question here is trivial by bash => you will find that n = 3 works. (If you are a quick guess + checker, you might've found that right of the bat quickly, as row 3 is 1, 3, 3, 1 which has an average entry of 2.)
