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

## Tags » 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

#### 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

#### 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

#### 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

#### 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

#### 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