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To win ‘In the bag’ in the least possible rounds you must be willing to sacrifice perfect scores for just ‘good’ scores. This will mean you only get 100 extra points each turn but it’s 50 points that you would lose, trying for a perfect score each round. The best way to get a good score is to go with common sense after 3 turns (very good number for an average which is what you are finding). All you must do is find an average for each colour and put it in. Remember though, that if you see a colour once put it in because it would have to be pretty badly glitched for it not to turn up.