Schweitzer Competition: A Selection

The Miklós Schweitzer Memorial Competition is a contest for university students in Hungary, held each fall since 1949 by the János Bolyai Mathematical Society. It is named for Miklós Schweitzer (1923–1945), a gifted young mathematician who was killed in the last months of the Second World War. Competitors get about ten days for ten or so problems set by research mathematicians, across analysis, algebra, number theory, combinatorics, probability, geometry and topology. They may look things up in books, but may not ask anyone for help. This page is a selection: from each year we include only the problems we could solve completely and check, with a link to the official problem, a topic label, hints and our own solution. The problem sets are hosted on Miklós Maróti's Schweitzer page at the University of Szeged, and results are posted on the Bolyai Society's competition page. Read more about the competition.

About these pages. The Schweitzer problems are © the János Bolyai Mathematical Society. We don't copy or translate them: read each one at the official link, in the committee's problem sheets hosted on Miklós Maróti's page at the University of Szeged. Some years are in Hungarian only. The topic labels, hints and solutions are our own work, written from scratch. They are not official solutions.

Years

Every problem

Problem	Topic	Area	Level	Solution
2023 P5	Algebra: counting word maps with fixed constants in a group	Algebra	2	Ready
2023 P9	Analysis: steep polynomials inside a closed finite-codimension subspace	Analysis	2	Ready
2023 P11	Probability: random points and the tightest triangle around them	Probability, Geometry	3	Ready
2022 P2	Linear algebra: matrices adding to the identity, with singular weightings	Linear algebra, Algebra	2	Ready
2022 P4	Number theory: the smallest positive moment of integer polynomials	Number theory, Analysis	3	Ready
2022 P5	Topology: disjoint segments chosen on every line of the plane	Topology, Geometry	3	Ready
2022 P9	Analysis: an arc of positive length generates the plane	Analysis, Geometry	2	Ready
2021 P9	Probability: two players guessing the same random subset	Probability, Combinatorics, Analysis	2	Ready
2020 P2	Analysis: an irrational rotation, wobbled by a periodic function	Analysis, Topology	2	Ready
2020 P11	Analysis: a divergence-free shift cannot lower a radial integral	Analysis	2	Ready
2019 P5	Geometry: halfspaces cutting out a convex body, with margin	Geometry, Analysis	2	Ready
2019 P7	Complex analysis: critical points inside a one-piece level curve	Analysis, Topology	2	Ready
2019 P8	Analysis: integrable differences force an integrable function	Analysis	2	Ready
2018 P6	Number theory: Gaussian periods and fourth powers modulo 13	Number theory, Algebra	3	Ready
2017 P8	Probability: binary digits that secretly drive a random walk	Probability	1	Ready
2017 P10	Probability: base-16 digits, a smooth sum and a Cantor dust	Probability, Analysis	1	Ready
2016 P9	Probability: weights at most one, and a symmetry trick	Probability, Geometry	2	Ready
2016 P10	Probability: spreading random points on a sphere to maximize distance	Probability, Geometry, Analysis	3	Ready
2015 P8	Analysis: arithmetic and geometric means in a functional equation	Analysis	2	Ready
2014 P2	Analysis: overlapping intervals and the lengths of their unions	Analysis, Combinatorics	2	Ready
2014 P4	Number theory: how fast ordered factorizations pile up	Number theory, Combinatorics, Analysis	3	Ready
2014 P5	Number theory: irreducible elements of an imaginary quadratic ring	Number theory, Algebra	2	Ready
2014 P8	Analysis: power series tails versus low-degree polynomials	Analysis	2	Ready
2014 P11	Probability: a random sine sum settles into the Cauchy law	Probability, Analysis	3	Ready

Try our original challenge problems · All competition pages