# Fifteen schoolgirls spread (5X3) across a week, a pair of qubits, and a rainbow of four basic colors: Common Patterns

LSU Department of Physics & Astronomy

A recreational puzzle posed 175 years ago of 15 schoolgirls to walk three abreast to school for seven days of the week so that no girl sees a friend repeated in her row has links to many areas of mathematics: combinatorics, finite projective geometries, design and coding theory, etc. A link can also be made to states and operators of two qubits in today's quantum information, those Lie algebras and groups also providing a systematic way to get the required arrangements of the girls. These patterns, that can be further linked to four-color vision and analogs in acoustics and sound, will be discussed.