MathDB

6

Part of 2010 India IMO Training Camp

Problems(1)

Indian Team Selection Test 2010 ST2 P3

Source:

5/22/2010
Let n≥2n\ge 2 be a given integer. Show that the number of strings of length nn consisting of 0′0's and 1′1's such that there are equal number of 0000 and 1111 blocks in each string is equal to 2(n−2⌊n−22⌋)2\binom{n-2}{\left \lfloor \frac{n-2}{2}\right \rfloor}
floor functioninductioncombinatorics unsolvedcombinatorics