a) There is a 100% successful strategy: Depending on whether person C has a red or a blue hat, person A and person B answer 'pass' in a different order, thereby telling C which colour his/her hat is. (Thanks to Ruth for this solution!) b) The best strategy is given by the first person passing unless he sees two red hats, in which case he guesses the colour. If the second person sees that the third person has a red hat, she knows that her own hat is blue. If the third person's hat is blue, she passes too. The third person can now determine the colour of their hat to be blue with certainty. So the team will only loose in one eigth of all cases.