4

Part of 2011 India Regional Mathematical Olympiad

Problems(2)

Indian RMO 2011: Question 4

Source:

20

-sided convex polygon

K

, with vertices

A_1, A_2,...,A_{20}

in that order. Find the number of ways in which three sides of

K

can be chosen so that every pair among them has at least two sides of

K

between them. (For example

(A_1A_2, A_4A_5, A_{11}A_{12})

is an admissible triple while

(A_1A_2, A_4A_5, A_{19}A_{20})

4 digit numbers from {0,1,...,5} [RMO2-2011, India]

Source:

Find the number of 4-digit numbers with distinct digits chosen from the set

\{0,1,2,3,4,5\}

in which no two adjacent digits are even.