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Pascal's Triangle

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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 2. Find $n$.

Feb 13, 2024

#1
+1624
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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 $${2^n\over{n+1}}=2$$

Cross multiplying, you get $$2^n=2n+2$$. 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.)

Feb 13, 2024

#1
+1624
+2
Additionally, row n has n + 1 terms, so we know from the problem that $${2^n\over{n+1}}=2$$
Cross multiplying, you get $$2^n=2n+2$$. 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.)