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标题: 6个球 [打印本页]

作者: fzy 时间: 2005-10-3 21:04
标题: 6个球

难度：++

有6个一样大小的球，红色，绿色，蓝色各两个。每种颜色的两个球都是一个15克，一个16克。用一座无砝码，无刻度的天平称两次，能不能找出3个重球？

作者: sean9991 时间: 2005-10-3 22:15
标题: 回复：6个球

Let the balls be R1, R2, G1, G2, B1, and B2.

First, test R1, G1 against R2, B1. There are two cases:www.ddhw.com

1. Balanced, each group consists of 1 heavy and 1 light ball. Then test G1 against G2. WLOG, if G1 > G2, then R1 < R2, B1 < B2.www.ddhw.com

2. WLOG, assume R1 + G1 > R2 + B1, therefore R1 > R2 and G1 >= B1. Then test B1, G1 against B2, R2. Three sub-cases:www.ddhw.com

a. B1 + G1 = B2 + R2. Then B1 < B2, G1 > G2.www.ddhw.com

b. B1 + G1 < B2 + R2. Then B1 < B2, G1 < G2.

c. B1 + G1 > B2 + R2. Then B1 > B2, G1 > G2.

作者: 野菜花 时间: 2005-10-3 22:32
标题: 回复：6个球

Let the 6 balls be H, H', G, G', B, B'.

1st weigh: H+G and H'+B

if H+G>H'+B

2nd weigh: G and B':

if G>B': H,G,B heavier

if G=B': H, G, B' heavier

if G

If H+G=H'+B

2nd weigh: H and H'

if H>H': H, G',B heavier

if H

If H+Gwww.ddhw.com

作者: fzy 时间: 2005-10-4 06:29
标题: 回复：6个球

Both solutions are correct, but I like the second one better, because it is a minimal solution: the second time there is only one ball on each side.

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