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 2006-05-25, 16:21 #1 mfgoode Bronze Medalist     Jan 2004 Mumbai,India 205210 Posts 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
 2006-05-25, 17:04 #2 alpertron     Aug 2002 Buenos Aires, Argentina 101101011102 Posts 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.
 2006-05-25, 18:39 #3 Citrix     Jun 2003 22×397 Posts 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
 2006-05-25, 19:10 #4 alpertron     Aug 2002 Buenos Aires, Argentina 2·727 Posts I found the drawing features of Tex very interesting: $\Large\hspace{5}\unitlength{1}\picture(150,150){~(50,50){\circle(100)}~(100,50){\circle(100)}~(75,100){\circle(100)}(c75,120){37}(c75,75){33}(c50,86){35}(c25,50){356}(c100,86){36}(c75,30){39}(c125,50){310}(c10,135){34}(c130,140){34a}(c140,7){33e}(c10,7){32h}}$ Sorry but spoiler and tex tags are incompatible.
 2006-05-25, 22:17 #5 victor     Oct 2005 Fribourg, Switzerlan 22·32·7 Posts If you really don't want to spoil, give us a link : answer ;)
2006-05-25, 22:28   #6
Xyzzy

Aug 2002

72×173 Posts

Quote:
 Originally Posted by alpertron $\Large\hspace{5}\unitlength{1}\picture(150,150){~(50,50){\circle(100)}~(100,50){\circle(100)}~(75,100){\circle(100)}(c75,120){37}(c75,75){33}(c50,86){35}(c25,50){356}(c100,86){36}(c75,30){39}(c125,50){310}(c10,135){34}(c130,140){34a}(c140,7){33e}(c10,7){32h}}$
Very cool!

 2006-05-26, 01:22 #7 davar55     May 2004 New York City 5×7×112 Posts Using the Inclusion-Exclusion Principle, the answer can be immediately computed as: 100 - (73+28+21-12-9-8+3) == 100 - 96 == 4 -- davar55
 2006-05-26, 07:10 #8 mfgoode Bronze Medalist     Jan 2004 Mumbai,India 40048 Posts 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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