The Question
Each number from the set {1,2,3,4,5,6,7,8,9} is coloured either red or blue according to the following rules:
i) The number 4 is red;
ii) If two numbers x, y have different colours and x + y < 9, then the number x + y is coloured blue;
iii) If two numbers x, y have different colours and x.y < 9, then the number x.y is coloured red
Find all possible colour arrangements.
This is at the level of a secondary national mathematics competition.
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