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Anton Petrunin
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We discuss a recursive formula for number of spanning trees in a graph. The paper is written primary for school students.
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No two rainbows are the same. Neither are two packs of Skittles. Enjoy an odd mix!. Using an interpretation via spatial random walks, we quantify the probability that two randomly selected packs of Skittles candy are identical and determine the expected number of packs one has to purchase until the first match. We believe this problem to be appealing for middle and high school students as well as undergraduate students at University.
An introduction to the On-Line Encyclopedia of Integer Sequences (or OEIS, https://oeis.org) for graduate students in mathematics
We introduce and analyze several variations of Penneys game aimed to find a more equitable game.
This note is purely expository and is in Russian. We show how to prove interesting combinatorial results using the local Lovasz lemma. The note is accessible for students having basic knowledge of combinatorics; the notion of independence is defined and the Lovasz lemma is stated and proved. Our exposition follows `Probabilistic methods of N. Alon and J. Spencer. The main difference is that we show how the proof could have been invented. The material is presented as a sequence of problems, which is peculiar not only to Zen monasteries but also to advanced mathematical education; most problems are presented with hints or solutions.
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