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.)

[Technical note: When the following solution was posted, the puzzle read "...every bullet went over 3 PEOPLE'S heads before it killed another person..." The puzzle has since been updated to disallow this solution.]

This solution has zero villagers, thanks to barbarian stupidity and the concept of "friendly fire". The barbarians practiced the old Greek formation of the phalanx (literally, "a log of wood") and formed themselves around the village in four columns of eight men. (The barbarians are around the village in the sense that there are barbarians to the east, north, south and west of the village). There is not a word in the puzzle that forbids this interpretation.

Barbarians B1 thru B8 lined up in a single column pointing at the village from the west. B1 fired east over B2,B3,B4 and killed B5. B2 fired east over B3,B4,B5 and killed B6. B3 fired east over B4,B5,B6 and killed B7. B4 fired east over B5,B6,B7 and killed B8. B5 thru B8 were confused. B5 fired fired west over B4,B3,B2 and killed B1. B6 fired west over B5,B4, B3 and killed B2. B7 fired west over B6,B5,B4 and killed B3. B8 fired west over B7,B6,B5 and killed B4.

Barbarians B9 thru B16 lined up in a single column pointing at the village from the south. B9 fired north over B10,B11,B12 and killed B13. B10 fired north over B11,B12,B13 and killed B14. B11 fired north over B12,B13,B14 and killed B15. B12 north fired over B13,B14,B15 and killed B16. B13 thru B16 were confused. B13 fired south over B12,B11,B10 and killed B9. B14 fired south over B13,B12,B11 and killed B10. B15 fired south over B14,B13,B12 and killed B11. B16 fired south over B15,B14,B13 and killed B12.

Barbarians B17 thru B24 lined up in a single column pointing at the village from the east. B17 fired west over B18,B19,B20 and killed B21. B18 fired west over B19,B20,B21 and killed B22. B19 fired west over B20,B21,B22 and killed B23. B20 west fired over B21,B22,B23 and killed B24. B21 thru B24 were confused. B21 fired east over B20,B19,B18 and killed B17. B22 fired east over B21,B20,B19 and killed B18. B23 fired east over B22,B21,B20 and killed B19. B24 fired east over B23,B22 and B21 and killed B20.

Barbarians B25 thru B32 lined up in a single column pointing at the village from the north. B25 fired south over B26,B27,B28 and killed B29. B26 fired south over B27,B28,B29 and killed B30. B27 fired south over B28,B29,B30 and killed B31. B28 fired south over B29,B30,B31 and killed B32. B29 thru B32 were confused. B29 fired north over B28,B27,B26 and killed B25. B30 fired north over B29,B28,B27 and killed B26. B31 fired north over B30,B29,B28 and killed B27. B32 fired north over B31,B30,B29 and killed B28.





Edited on January 28, 2004, 5:57 pm

Posted by Penny on 2004-01-28 15:57:56