Question 40
A quadruple $(a, b, c, d)$ of positive integers with $a \leq b \leq c \leq d$ is called good if we can colour every integer red, blue, green or purple such that
- of every $a$ consecutive integers at least one is red;
- of every $b$ consecutive integers at least one is blue;
- of every $c$ consecutive integers at least one is green;
- of every $d$ consecutive integers at least one is purple.
Determine all good quadruples with $a=2$.
- of every $a$ consecutive integers at least one is red;
- of every $b$ consecutive integers at least one is blue;
- of every $c$ consecutive integers at least one is green;
- of every $d$ consecutive integers at least one is purple.
Determine all good quadruples with $a=2$.