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 Thirty two barbarians (Posted on 2004-01-28)
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.)

 No Solution Yet Submitted by Gamer Rating: 3.0000 (6 votes)

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 re: upper bound, same assumptions | Comment 15 of 34 |
(In reply to upper bound by SilverKnight)

A sort of better upper bound... same number of villagers, but can handle up to 40 barbarians.

And clearly, we can remove any one of these villagers, and still be able to deal with at least 32 barbarians... so this provides an upper bound of 23.

Same assumptions:
Assuming that ONLY villagers (not barbarians) can be killed.
Assuming that we can shoot the same villagers more than once.
Assuming that not all villagers must be killed.

Here, we've got still got 24 villagers in such a way that up to 40 barbarians can line up on the outside and shoot (satisfying the constraints of the problem).

There are 20 lines of consequence:

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MNOP
QRST
CJNU
DKOV
AFRW
BGSX
BDHL
AGKP
CFOT
EJSV
INRX
MQUW
IECA
MJFB
QNGD
URKH
WSOL
XVTP

`. . . . . . . . . . . . . .. . . . . . . . . . . . . .. . . . . . . . . . . . . .. . . . . A . B . . . . . .. . . . C . . . D . . . . .. . . E . F . G . H . . . .. . I . J . . . K . L . . .. . . . . . . . . . . . . .. . M . N . . . O . P . . .. . . Q . R . S . T . . . .. . . . U . . . V . . . . .. . . . . W . X . . . . . .. . . . . . . . . . . . . .. . . . . . . . . . . . . .. . . . . . . . . . . . . .`

Edited on January 29, 2004, 12:55 am
 Posted by SilverKnight on 2004-01-29 00:31:00

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