Five tents, each of a different colour, are to be placed on five different campsites. The five campsites are arranged as shown, with each pair of campsites connected by a path. The number on each path indicates the number of minutes it takes to walk along that path.
Jared wants to start at the blue tent, and take a walk along some of the paths passing the tents in the order green, white, yellow, red, and yellow, before returning to the blue tent.
If Jared wants the total time that he spends walking to be as small as possible, what colour tent(s) should be put in campsite \(C\)?
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This problem was inspired by a past Beaver Computing Challenge (BCC) problem.