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problem #3: Loopy Subsets

problem #3: Loopy Subsets

Call a set S “loopy” if it contains |S|. A set S is minimally loopy if it is loopy but contains no loopy proper subset. Find the number of minimally loopy subsets of {1,2,3,…,n}.

by jkgnow October 23, 2021

problem #2: Empty Squares on Peaceful Chessboards (IMO 2014 P2)

problem #2: Empty Squares on Peaceful Chessboards (IMO 2014 P2)

Let $n \ge 2$ be an integer. Consider an $n \times n$ chessboard consisting of $n^2$ unit squares. A configuration of $n$ rooks on this board is $\textit{peaceful}$ if every row and every column contains exactly one rook. Find the greatest…

by jkgnow June 2, 2021October 12, 2021

problem #1: The Happy Ending Problem

problem #1: The Happy Ending Problem

Show that given any 5 points in the plane, no 3 of which are collinear, 4 of them must form the vertices of a convex quadrilateral.

by jkgnow June 1, 2021July 20, 2021

An Elementary Solution to The Isoperimetric Problem

An Elementary Solution to The Isoperimetric Problem

Why circles are the best shape.

by jkgnow April 16, 2021February 2, 2022

Recursions, Differential Equations, and Unexpected Expectations

Recursions, Differential Equations, and Unexpected Expectations

You won’t believe the answer to this one! Statisticians will hate you!

by jkgnow February 13, 2021April 13, 2021

Intuition vs. Technique: On Taking Paths Around Circles

Intuition vs. Technique: On Taking Paths Around Circles

Two ways to solve a problem (and why I like my way better).

by jkgnow August 5, 2020May 31, 2021

Light Rays and a Minimum Perimeter Triangle

Light Rays and a Minimum Perimeter Triangle

Using physics to solve a math problem.

by jkgnow May 2, 2020May 31, 2021

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