For some reason, British policemen on foot duty will wear either a flat cap (in Scotland) or a helmet (elsewhere), whereas policewomen wear bowler hats. I have always wondered why this is so, and in particular I feel it is quite a bit unfair that men aren't allowed to wear bowlers, which are clearly much cooler than the alternatives.
Today, walking home from a fireworks concert (as you do), Camilla, Mary and I walked past a group of police officers, with a woman wearing a bowler, and some men wearing flat caps, and in an impressive act of bravery, Mary walked up to them and asked why only the women wear bowlers.
After initial friendly laughter, the first policeman said it is because the men's heads are all flat. The second policeman said that it might be a bit sexist, but it's a tradition. However, he seemed to think that we thought the flat caps were cooler, so when we explained that we really prefer the bowlers, he seemed a bit disappointed. The policewoman was very pleased though, which promted the third policeman to say that we shouldn't have told her that, as her head was already too big as it was. An then the second policeman, which seemed to be the leader of the group, repeated that it's because it's tradition.
Obviously, "because it's tradition" isn't a proper answer, or at least it leads to a new question, "how did it become a tradition?", but I would still like to commend the Edinburgh police for their friendly attitude.