For instance :

a | b | c | d |

d | c | b | a |

b | a | d | c |

c | d | a | b |

By tradition, one is made of latin letters and the other of greek letters, to build a

aα | bβ | cγ | dδ | as the well known 10×10 graeco-latin square in the picture, said to be impossible by Euler, and only discovered in 1960 ! | |

dβ | cα | bδ | aγ | ||

bγ | aδ | dα | cβ | ||

cδ | dγ | aβ | bα |

Merge three 4×4 latin squares to build an "arabo-graeco-latin" square, build of combinations of arabic numbers 1234, greek letters αβγδ and latin letters abcd, every symbol once and only once in every row and column, and every symbol pair only once. Solution Details