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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. There is an interesting historic link of this problem to the 1938
Bombay Science Congress, resulting in a branch of mathematics born in
India. The problem can also be linked 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-colour vision
and analogs in acoustics and sound, will be discussed. They may be
useful for manipulating states and operators of a pair of qubits, with
generalization also to multiple qubits. |