10 soldiers were captured and thrown into a prisoner’s camp towards the end of a war. The captain of the camp, a kind man, was ordered by his superior to execute all 10 of the prisoners the next day, as the war is due to be over any days now.
He decided to offer the prisoners seats at the captain’s table during the last supper. They all hit off really well, the captain realised that they were all very intelligent men, and they would have been good friends if not for the war.
After supper, he brought the prisoners out in the open so that everyone at the camp could see and hear his announcement.
He told the prisoners that they were due to be executed the next day, however due to the imminent end of the war, he felt that the killing was senseless. However orders were orders, and he could only offer them a way out through a game of chance.
He explained that come next day, he would line the prisoners up so that they’d all face the same direction, as such that they would only be able to see the prisoners standing in front of them.
The prisoners shall be blindfolded, and a hat would be placed on top of each of their heads. On each hat would be a black or a white banner chosen at random. Then all the prisoners’ blindfolds shall be removed.
They would not be able to see their own banners, but they would be able to see all the banners in front of them clearly. They’re not allowed to turn around either to see the banners behind.
Then, he shall approach each of the prisoners, from the back to the front, and ask each one to guess what colour their own banner is. The prisoner is only allowed to say the colour of their banner and nothing else, or all the prisoners will be executed.
If the prisoner can correctly guess their own banner, they would be free to go; otherwise they’d be executed on the spot.
Overnight, the 10 prisoners sat together and discussed a strategy.
The puzzle is - what strategy should they use to save most of their lives? What’s the minimum number of prisoners they could save?