Meeting Name Cards I
4 people (ABCD) are at a table for a meeting. Sketch a way to place the name cards (abcd) such that they’re all mismatched. Then rotate the table such that at least 2 people have the right name cards.
Angles of Intersecting Chords
Here's a problem based on an obscure theorem about angles of intersecting chords.
Factors of Non-Integers
Problem of the Week #93: Monday June 23rd, 2025As before, these problems are the results of me following my curiosity, and I make no promises regarding the topics, difficulty, solvability…
Distance Sums
If we place 3 points on a line segment of length 1 and add up all pair-wise distances between them, what’s the biggest sum we can get?
Centers at a Corner
Sketch the area reachable by the midpoint of a line segment of length 1, if its entire length is confined to the first quadrant (x>=0 and y>=0) of a Cartesian plane, and one of its end points must be on the x- or the y- axis.
Pronic Fractions
A pronic number is a natural number of the form n(n+1), where n is also a natural number. Let’s call the reciprocal of a pronic number a pronic fraction.
Grid Colouring
How many ways are there to colour a 3x3 grid using 2 colours such that no rectangle in the grid has the same colour in all 4 corners?
Combined Chords
Two circles intersect at P and Q. Let’s call line AB through P a combined chord if AP and PB are chords of the respective circles. Let’s define the split product of AB as the length of AP times the length of PB.
Linear Flooring
The floor function [a] denotes the greatest integer less than or equal to a. For x and y strictly between 0 and 1, the probability of [2x]+[2y] being 1 is 1/2.
Intersecting Circles
If we draw pairs of circles of the same sizes centered at two distinct points and mark where each pair of circles intersects, we’d trace out a straight line.