Timeline

A cycle-following strategy turns an almost impossible search into a surprisingly hopeful one.

How far can an army of pegs advance when every move must be a jump?

Two missing corners, thirty-one dominoes, and one coloring that settles everything.

One prize, three doors, and an informed host: should you switch?

Nine distinguished points of every triangle quietly share a single circle.

A practical way to search for the quantity a legal move cannot change.

Adjacent angle trisectors of an arbitrary triangle form an equilateral triangle.

A seductive expected-value argument seems to say that switching is always better.

Orbit thinking, Burnside’s lemma, and the warning signs of accidental overcounting.

Count routes through a grid by forgetting the picture and remembering only the moves.

A short factor-stripping loop is enough when every discovered divisor changes the remaining problem.

Why one auxiliary line can be more valuable than a page of algebra.

A first exercise in turning iteration into arithmetic with inclusion–exclusion.