For certain cardinals [lambda] and [kappa] a colouring P:[[lambda]]2-->[lambda] is constructed such that if X [epsilon][[lambda]][lambda] and Q:[[kappa]]2-->[lambda], then there is a one-to-one function i:[kappa]-->X such that P(i"A)=Q(A) for every A[epsilon][[kappa]]2. Additional results are obtained.
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