MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - Other Middle and High School Contests
Math Prize For Girls Problems
2012 Math Prize For Girls Problems
14
14
Part of
2012 Math Prize For Girls Problems
Problems
(1)
Math Prize 2012 Problem 14
Source:
9/24/2012
Let
k
k
k
be the smallest positive integer such that the binomial coefficient
(
1
0
9
k
)
\binom{10^9}{k}
(
k
1
0
9
)
is less than the binomial coefficient
(
1
0
9
+
1
k
−
1
)
\binom{10^9 + 1}{k - 1}
(
k
−
1
1
0
9
+
1
)
. Let
a
a
a
be the first (from the left) digit of
k
k
k
and let
b
b
b
be the second (from the left) digit of
k
k
k
. What is the value of
10
a
+
b
10a + b
10
a
+
b
?
quadratics