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速度问个包子题
[版面:大脑工作室][首篇作者:vonion] , 2010年07月13日21:07:02 ,552次阅读,3次回复
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vonion
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发信人: vonion (fish smell pork slip), 信区: BrainTeaser
标  题: 速度问个包子题
发信站: BBS 未名空间站 (Tue Jul 13 21:07:02 2010, 美东)

Given a big cube consisting of 1,000 smaller cubes, 10 on each side (imagine
a Rubik’s cube but instead of 3 little cubes on each side, there are 10).
Paint all 6 outer surfaces on the big cube the color red. Now take apart the
big cube, and examine the 1,000 small cubes individually.

a)    Out of 1,000, how many small cubes have 4 surfaces painted red? 3
surfaces? 2 surfaces? 1 surface? 0 surfaces?

b)    Given a big cube with n smaller cubes on each side, so that there are
n3 smaller cubes total. Write 5 separate formulas, each as a function of n,
for the total number of smaller cubes with 4, 3, 2, 1, and 0 surfaces
painted red.
--

※ 来源:·WWW 未名空间站 海外: mitbbs.com 中国: mitbbs.cn·[FROM: 24.184.]

 
FAXMachine
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发信人: FAXMachine (黑肉曾经的我是哀木涕), 信区: BrainTeaser
标  题: Re: 速度问个包子题
发信站: BBS 未名空间站 (Tue Jul 13 21:30:10 2010, 美东)

a)

4s: 0
3s: 8
2s: 12*(10-2)=96
1s: 8*8*6=384
0s: 8^3=512
验证sum=1000


b)
n=1: 6s=1 rest=0
n=2: 3s:8 rest=0
n>=3:
4s: 0
3s: 8
2s: 12*(n-2)
1s: 6*(n-2)^2
0s: (n-2)^3
【 在 vonion (fish smell pork slip) 的大作中提到: 】
Given a big cube consisting of 1,000 smaller cubes, 10 on each side (imagine
a Rubik’s cube but instead of 3 little cubes on each side, there are 10).
Paint all 6 outer surfaces on the big cube the color red. Now take apart the
big cube, and examine the 1,000 small cubes individually.

a)    Out of 1,000, how many small cubes have 4 surfaces painted red? 3
surfaces? 2 surfaces? 1 surface? 0 surfaces?

b)    Given a big cube with n smaller cubes on each side, so that there are
n3 smaller cubes total. Write 5 separate formulas, each as a function of n,
for the total number of smaller cubes with 4, 3, 2, 1, and 0 surfaces
painted red.
--

※ 来源:·WWW 未名空间站 海外: mitbbs.com 中国: mitbbs.cn·[FROM: 24.184.]



--

※ 来源:·BBS 未名空间站 海外: mitbbs.com 中国: mitbbs.cn·[FROM: 76.189.]

 
vonion
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发信人: vonion (fish smell pork slip), 信区: BrainTeaser
标  题: Re: 速度问个包子题
发信站: BBS 未名空间站 (Tue Jul 13 21:44:21 2010, 美东)

Baozi sent. Thx!

【 在 FAXMachine (黑肉曾经的我是哀木涕) 的大作中提到: 】
: a)
: 4s: 0
: 3s: 8
: 2s: 12*(10-2)=96
: 1s: 8*8*6=384
: 0s: 8^3=512
: 验证sum=1000
: b)
: n=1: 6s=1 rest=0
: n=2: 3s:8 rest=0
: ...................



--

※ 来源:·WWW 未名空间站 海外: mitbbs.com 中国: mitbbs.cn·[FROM: 24.184.]

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