  A recreational problem from nearly two centuries ago has featured prominently
in recent times in the mathematics of designs, codes, and signal processing.
The number 15 that is central to the problem coincidentally features in areas
of physics, especially in today's field of quantum information, as the number
of basic operators of two quantum spins ("qubits"). This affords a 1:1
correspondence that we exploit to use the well-known Pauli spin or Lie-Clifford
algebra of those fifteen operators to provide specific constructions as posed
in the recreational problem. An algorithm is set up that, working with four
basic objects, generates alternative solutions or designs. The choice of four
base colors or four basic chords can thus lead to color diagrams or acoustic
patterns that correspond to realizations of each design. The Fano Plane of
finite projective geometry involving seven points and lines and the tetrahedral
three-dimensional simplex of 15 points are key objects that feature in this
study.
