Revenge of the Hats And Scarves!

A team of 1999 students is involved in a game: each of them puts on a cap of one of 7 already-known colours and then on hearing the whistle, each team member must put on one of the coloured scarves. For each team member with matching colour scarves and hats the team receives one point (there is a sufficient amount of scarves of any colour; each person cannot see the colour of his own hat but can see everyone else's, not being able to give away any information). What is the maximum number of points that the team can guarantee to earn, having decided before the game on a strategy?


The answer is 285.

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