Solutions to review problems

This page is going to contain some of the solutions I submit to mathematical periodicals with problem sections such as Mathematical Reflections and The American Mathematical Monthly. Problems are usually rewritten in order to avoid excessive quoting and often to homogenize the notations used in a problem and its solution.

I don't put up solutions on this site prior to the discussion of the problem in the respective magazine, so usually they won't appear here directly after the deadline is over.

Mathematical Reflections

The American Mathematical Monthly

One day I might add a solution to #11397 (I am still pondering whether to write up a proof of Karamata...).

Project PEN (Problems in Elementary Number Theory)


This was a Vietnamese project at creating a journal for mathematical problems. Sadly, it has not kicked off.

Problems from the Book (diverse mathematical problems)

QED-Mathematikolympiade (click here for a description of this context)

Solutions to several problems in German

Other problems and solutions

Some AoPS/MathLinks solutions

a graph with 2n+1 vertices | some inequalities for 2 triangles | a combinatorial identity from number theory | an Oddtown variation for acyclic graphs | a nonstandard inequality | generalizing a BMO problem | ARO 2005 10.2 combinatorics | an unwieldy proof for an unwieldy combinatorial identity | generalizing the ordered Shapiro inequality | a double count | rearrangement inequality redux |

All sources: Mathematical Reflections, American Mathematical Monthly, QEDMO, PFTB and PEN.

Solutions to review problems

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Darij Grinberg