MathDB

Indian Team Selection Test 2010 ST2 P3

Source:

May 22, 2010

floor functioninductioncombinatorics unsolvedcombinatorics

Problem Statement

Let

n\ge 2

be a given integer. Show that the number of strings of length

n

consisting of

0'

s and

1'

s such that there are equal number of

00

and

11

blocks in each string is equal to

2\binom{n-2}{\left \lfloor \frac{n-2}{2}\right \rfloor}