MathDB

A quadruple

(a; b; c; d)

of positive integers with

a \leq b \leq c \leq d

is called good if we can colour each integer red, blue, green or purple, in such a way that

i

of each

a

consecutive integers at least one is coloured red;

ii

of each

b

consecutive integers at least one is coloured blue;

iii

of each

c

consecutive integers at least one is coloured green;

iiii

of each

d

consecutive integers at least one is coloured purple. Determine all good quadruples with

a = 2.

Problem Statement