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Domination Number of a Graph with Given Minimum Degree.

I plan to discuss a characteristic of a graph, known as “domination number/dominating set”. An Olympiad problem will be discussed and also an interesting result of Alon and Spencer, given in their book “The Probabilistic Method”. 726 more words

Math Olympiads

IMO 2019 Shortlist, problem A4.

Problem. (A4, IMO SL, 2019) Let be a positive integer and be real numbers such that

Define the set by

Prove that, if is non empty, then… 77 more words

Math Olympiads

A Family of Sets. Miklós Schweitzer 2010, Problem 3.

Problem 3 (Miklós Schweitzer 2010). Let be distinct subsets of the base set complying to the following condition

for any Find the maximum value of… 148 more words

Math Olympiads

Binary Strings With the Same Spheres! IMO 2016 Shortlist, C1.

I have come across this problem many times since it appeared in public. It somehow didn’t attract me, but I knew, it was not difficult for an IMO level problem. 438 more words

Math Olympiads

Very Convex Function. USAMO 2000, Problem 1.

Problem (USAMO 2000, p1). Call a real-valued function very convex if

holds for all real numbers and . Prove that no very convex function exists. 489 more words

Math Olympiads

An AMM Problem by Paul Erdös. Number of Certain Objects in a Converging Series.

Flipping through some college problems I saw this gem. The name of Paul Erdos added additional curiousity.

Problem (AMM , E3000, Paul Erdös). Let be an infinite sequence and suppose converges. 242 more words

Math Olympiads

When Graphs Make Things Worse. IMO 2005 Shortlist, C1.

Have you ever experienced a situation when interpreting of a problem in graph theory language makes things worse? Here is an example.

Problem C1, IMO 2005 Shortlist… 543 more words

Math Olympiads