A square array made by combining objects of two types such that the first and second elements
form Latin squares. Euler squares are also known
as Graeco-Latin squares, Graeco-Roman squares, or Latin-Graeco squares.
For many years, Euler squares were known to exist for , 4, and for every odd except . Euler's
Graeco-roman squares conjecture maintained that there do not exist Euler squares
of order
for , 2, .... However, such squares were
found to exist in 1959, refuting the conjecture. As
of 1959, Euler squares are known to exist for all except and .
objects of two types such that the first and second elements
form Latin squares. Euler squares are also known
as Graeco-Latin squares, Graeco-Roman squares, or Latin-Graeco squares.
, 4, and for every odd 
except 
. Euler's
Graeco-roman squares conjecture maintained that there do not exist Euler squares
of order 
for 
, 2, .... However, such squares were
found to exist in 1959, refuting the conjecture. As
of 1959, Euler squares are known to exist for all 
except 
and 
.
