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Because the problem is devised in such a way that the defender cannot be distinguished with one of the attackers, for all theoretical purposes the defender acts as one of the attackers but inverts the message of the other attacker. Since no message can distinguish the defender from one of the attackers it is impossible to coordinate. This can be seen by simply removing one attacker and treating the problem as two players that must coordinate but in which one always can thwart any coordination(through error or intent). The only solution to the problem is to be able to distinguish the defender from the attacker which solves the problem trivially.
These problems show up in many games such as chess where one player can always make a move that prevents the other from achieving an end goal such as perpetual check and which external "rules" must be imposed to get around it.
==Engineering approaches==
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