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.)

If we had two circles with 32 people in each, properly aligned, the shooting could occur, so 64 is an upper bound for the answer, and of course, 32 is a lower bound.

After further reflection, having two lines of 8 people in the middle, and 32 around, would also allow for a solution, so I'd say "48 or less".

Posted by e.g. on 2004-01-28 14:45:22