2

Part of 2015 Danube Mathematical Competition

Problems(2)

5 subsets with some propriety...

Source: Danube Mathematical Competition,Juniors #2

Consider the set

A=\{1,2,...,120\}

M

A

|M|=30

.Prove that there are

5

different subsets of

M

,each of them having two elements,such that the absolute value of the difference of the elements of each subset is the same.

combinatoricsnumber theoryabsolute value

a simple finite graph problem

Source: Danube 2015 p2

Show that the edges of a connected simple (no loops and no multiple edges) finite graph can be oriented so that the number of edges leaving each vertex is even if and only if the total number of edges is even

graph theorygraphcombinatoricsEven