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 
. 