MathDB

Math Prize 2012 Problem 14

Source:

September 24, 2012

quadratics

Problem Statement

Let

k

be the smallest positive integer such that the binomial coefficient

\binom{10^9}{k}

is less than the binomial coefficient

\binom{10^9 + 1}{k - 1}

. Let

a

be the first (from the left) digit of

k

and let

b

be the second (from the left) digit of

k

. What is the value of

10a + b