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Old 2006-05-25, 16:21   #1
mfgoode
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Question Aliens.


100 aliens attended the Intergalactic meeting on Earth.

73 had 2 heads
28 had 3 eyes.
21 had four arms.
12 had 2 heads and 3 eyes.
9 had 3 eyes and 4 arms.
8 had 2 heads and 4 arms.
3 had all 3 unusual features.
How many had none of these unusual features.?
Mally
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Old 2006-05-25, 17:04   #2
alpertron
 
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My solution is:


A = 1 head, 2 eyes, 2 arms
B = 1 head, 2 eyes, 4 arms
C = 1 head, 3 eyes, 2 arms
D = 1 head, 3 eyes, 4 arms
E = 2 heads, 2 eyes, 2 arms
F = 2 heads, 2 eyes, 4 arms
G = 2 heads, 3 eyes, 2 arms
H = 2 heads, 3 eyes, 4 arms

100 = A+B+C+D+E+F+G+H
73 = E+F+G+H
28 = C+D+G+H
21 = B+D+F+H
12 = G+H
9 = D+H
8 = F+H
3 = H

A = ?

D = 9-3 = 6
F = 8-3 = 5
G = 12-3 = 9
C = 28-6-9-3 = 10
B = 21-6-5-3 = 7
E = 73-5-9-3 = 56
A = 100-7-10-6-56-5-9-3 = 4

So the requested number of aliens is four.
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Old 2006-05-25, 18:39   #3
Citrix
 
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This is a simple question of sets. Add all the 3 sets, subtract the overlaping.
My answer is 4.


Last fiddled with by Citrix on 2006-05-25 at 18:40
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Old 2006-05-25, 19:10   #4
alpertron
 
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I found the drawing features of Tex very interesting:

\Large\hspace{5}\unitlength{1}\picture(150,150){~(50,50){\circle(100)}~(100,50){\circle(100)}~(75,100){\circle(100)}(c75,120){3$7}(c75,75){3$3}(c50,86){3$5}(c25,50){3$56}(c100,86){3$6}(c75,30){3$9}(c125,50){3$10}(c10,135){3$4}(c130,140){3$4a}(c140,7){3$3e}(c10,7){3$2h}}

Sorry but spoiler and tex tags are incompatible.
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Old 2006-05-25, 22:17   #5
victor
 
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If you really don't want to spoil, give us a link : answer ;)
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Old 2006-05-25, 22:28   #6
Xyzzy
 
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Quote:
Originally Posted by alpertron
\Large\hspace{5}\unitlength{1}\picture(150,150){~(50,50){\circle(100)}~(100,50){\circle(100)}~(75,100){\circle(100)}(c75,120){3$7}(c75,75){3$3}(c50,86){3$5}(c25,50){3$56}(c100,86){3$6}(c75,30){3$9}(c125,50){3$10}(c10,135){3$4}(c130,140){3$4a}(c140,7){3$3e}(c10,7){3$2h}}
Very cool!

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Old 2006-05-26, 01:22   #7
davar55
 
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Using the Inclusion-Exclusion Principle, the answer can be
immediately computed as:

100 - (73+28+21-12-9-8+3) == 100 - 96 == 4

-- davar55
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Old 2006-05-26, 07:10   #8
mfgoode
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Thumbs up Aliens.


All the answers given above are correct.

The Venn diagram given by Alpetron was what I was in search of but do not know how to use Tex. These were followed up by Mike and Vctor.

Citrix and Davar gave the short cuts.

Thanks to you Davar Im happy that you are now flexing your muscles!

Inclusion - Exclusion principle ? One for my note book!

Mally
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