Purple parity at a party
No musical chairs here. At this bash, you must guess the colour of your hat
Surabhi got tired of playing the same games at her birthday parties. Even musical chairs and passing the pillow get boring when you’ve played them 78 times. So for her 79th birthday, Surabhi’s mother dreamed up a new game.
Surabhi’s mother meets each new guest at the door and asks her to close her eyes. She gives the guest either a purple or an orange hat and dispatches her to stand in front of the previous guest to arrive. When everyone has arrived, there’s a long line in the room. The last guest in the line — the first to arrive — is at the end of the line.
Nobody knows what colour her own hat is. Nobody can turn around to see the hats behind her. But each denizen of the line can see the hats of all the denizens in front.
When everyone has arrived, the game begins, and it goes like this. Starting with the first guest to arrive, the one at the back of the line, Surabhi asks each in turn what colour her own hat is. If she gets it right, she gets a bar of chocolate. If not, Surabhi administers to her behind a loving kick.
Naturally, the guests want to minimise kicks and maximise chances of chocolate. The rules allow them to confer for a minute before the game begins, to come up with a strategy, though nobody is allowed to tell any other guest what colour her hat is.
Surabhi has special friends. Because with the strategy they used, there’d be a maximum of just one kick. The rest? Smooth, delicious chocolate.
What was the strategy they came up with?
For the answer, turn to P13