There is a small town situated by a barbarian colony. The population in this town is very small, but they live well. Upon seeing the villagers in this town so happy, a group of thirty two barbarians sneak up and position themselves around the city. All the barbarians fired at exactly the same time, and every bullet went over 3 villager's heads before it killed another person, including anyone who may have been shot already. If no villager was at the same place at the time (and all villagers were in the town) when the simultaneous shooting occurred, what is the fewest amount of villagers in the town? (Note: "Around" means actually around. A line going around the city would work, but one going out of the city would not.)

Why isn't the answer 16 peasants, it seems that the barbarians do not have to kill all the peasants, or only shoot each peasant only once, or even be randomly spaced themselves.
If the sixteen peasants form a 4X4 square and stand at regular intervals, and the barbarians line up around the perimeter of a 6 unit square encircling the peasants, doubling at the corners, and firing along the diaginals then the premisses of the problem are all met.
And 4 peasants survive.

Posted by bs on 2004-02-03 01:04:54