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发信人: ncode (真麻烦), 信区: BrainTeaser
标 题: Re: jiaoyou8认识的一个国内JP女生，专考12球问题.
发信站: BBS 未名空间站 (Mon Oct 13 12:34:57 2008)
from some forum - http://archive.tivocommunity.com/tivo-vb/history/topic/97075-1.html
looks like this was a competition for 8th graders (U.S.) Are they that smart really?
Number the balls 1 to 12. Weigh 1, 2, 3, and 4 against 5, 6, 7, and 8.
If (1, 2, 3, 4) and (5, 6, 7, 8) balance:
Weigh 9 and 10 against 11 and 8 (we know 8 is not the odd ball).
If (9, 10) and (11, 8) balance: then 12 is the odd one.
Weigh 12 against any other to find out if it is heavy or light.
If (9, 10) and (11, 8) do not balance: suppose 11 and 8 are heavier,
than 9 and 10; then either 11 is heavy, or 9 is light, or 10 is light.
Weigh 9 against 10; if they balance, 11 is heavy; if they do not,
the lighter of 9 and 10 is the odd ball.
(Similar argument if 11 and 8 are lighter than 9 and 10).
If (1, 2, 3, 4) and (5, 6, 7, 8) do not balance:
Suppose 5, 6, 7, and 8 are heavier than 1, 2, 3, & 4. Then: one of
(1, 2, 3, or 4) is light, or else one of (5, 6, 7, or 8) is heavy.
Weigh 1, 2, and 5 against 3, 6, and 9.
If they balance: then either 7 is heavy, or 8 is heavy, or 4 is light.
Weigh 7 against 8; if they balance, 4 is the odd ball, otherwise the
heavier of 7 and 8 is the odd ball.
If (1, 2, 5) and (3, 6, 9) do not balance: suppose 1, 2, and 5 are lighter
than 3, 6, and 9; then either 6 is heavy, or 1 is light, or 2 is light.
Weigh 1 against 2 to find out which one of the three choices is true.
Otherwise, suppose 1, 2, and 5 are heavier than 3, 6, and 9; then either 3
is light, or 5 is heavy.
Weigh 3 against (say) 2 to find out which of the two choices is true.
(Similar argument if 1, 2, and 5 are lighter than 3, 6, and 9).
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※ 修改:·ncode 於 Oct 13 12:40:37 2008 修改本文·[FROM: 204.194.]
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