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	<title>Comments on: Problem One: Aliens</title>
	<link>http://www.tenproblems.com/20061116/problem-one-aliens/</link>
	<description>Exploration, Calculation, Observation: Brain Teasers and Puzzles</description>
	<pubDate>Fri, 09 Jan 2009 20:29:55 +0000</pubDate>
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		<title>By: Venkat</title>
		<link>http://www.tenproblems.com/20061116/problem-one-aliens/#comment-3374</link>
		<dc:creator>Venkat</dc:creator>
		<pubDate>Mon, 08 Oct 2007 14:48:21 +0000</pubDate>
		<guid>http://www.tenproblems.com/20061116/problem-one-aliens/#comment-3374</guid>
		<description>yea - got 4 (with Venn Diagrams)</description>
		<content:encoded><![CDATA[<p>yea - got 4 (with Venn Diagrams)</p>
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		<title>By: mathieu</title>
		<link>http://www.tenproblems.com/20061116/problem-one-aliens/#comment-343</link>
		<dc:creator>mathieu</dc:creator>
		<pubDate>Sat, 03 Feb 2007 05:52:20 +0000</pubDate>
		<guid>http://www.tenproblems.com/20061116/problem-one-aliens/#comment-343</guid>
		<description>Using venn diagram you get the exact same result, check you drawings :). Here are the groups:

2 heads only: 56
3 eyes  only: 10
4 arms  only: 7
9 (12-3) had two heads and three eyes (no 4 arms)
6 (9-3) had three eyes and four arms (no 2 heads)
5 (8-3) had two heads and four arms (no 3 eyes)

this one remains the same:
3 had all three unusual features.

Let's verify the 3 first definition:
73 had two heads = 56 + 5 + 3 + 9
28 had three eyes = 10 + 6 + 3 + 9
21 had four arms = 7 + 5 + 6 + 3
...

Those groups forms a partition with total:
  56
+ 10
+  7
+  9
+  6
+  5
+  3
----
  96</description>
		<content:encoded><![CDATA[<p>Using venn diagram you get the exact same result, check you drawings :). Here are the groups:</p>
<p>2 heads only: 56<br />
3 eyes  only: 10<br />
4 arms  only: 7<br />
9 (12-3) had two heads and three eyes (no 4 arms)<br />
6 (9-3) had three eyes and four arms (no 2 heads)<br />
5 (8-3) had two heads and four arms (no 3 eyes)</p>
<p>this one remains the same:<br />
3 had all three unusual features.</p>
<p>Let&#8217;s verify the 3 first definition:<br />
73 had two heads = 56 + 5 + 3 + 9<br />
28 had three eyes = 10 + 6 + 3 + 9<br />
21 had four arms = 7 + 5 + 6 + 3<br />
&#8230;</p>
<p>Those groups forms a partition with total:<br />
  56<br />
+ 10<br />
+  7<br />
+  9<br />
+  6<br />
+  5<br />
+  3<br />
&#8212;-<br />
  96</p>
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	<item>
		<title>By: clevi</title>
		<link>http://www.tenproblems.com/20061116/problem-one-aliens/#comment-317</link>
		<dc:creator>clevi</dc:creator>
		<pubDate>Tue, 26 Dec 2006 04:58:05 +0000</pubDate>
		<guid>http://www.tenproblems.com/20061116/problem-one-aliens/#comment-317</guid>
		<description>With the help of venn diagram the alliens left with none of the above features are 13. How can we get 4 as the answer, please let me know.</description>
		<content:encoded><![CDATA[<p>With the help of venn diagram the alliens left with none of the above features are 13. How can we get 4 as the answer, please let me know.</p>
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		<title>By: xysk</title>
		<link>http://www.tenproblems.com/20061116/problem-one-aliens/#comment-312</link>
		<dc:creator>xysk</dc:creator>
		<pubDate>Tue, 19 Dec 2006 18:59:51 +0000</pubDate>
		<guid>http://www.tenproblems.com/20061116/problem-one-aliens/#comment-312</guid>
		<description>Four.

let h=heads, e=eyes, a=arms

there are:

 3 hea
 9 he only (12 total he - 3hea already counted)
 6 ae only ( 9 total ae - 3hea already counted) 
 5 ha only ( 8 total ae - 3hea already counted)
56 h  only (73 total h - (3hea + 9he + 5ha)counted)
10 e  only (28 total e - (3hea + 9he + 6ae)counted)
 7 a  only (21 total a - (3hea + 6ae + 5ha)counted)
----
96 of 100 aliens with features. Four remain.</description>
		<content:encoded><![CDATA[<p>Four.</p>
<p>let h=heads, e=eyes, a=arms</p>
<p>there are:</p>
<p> 3 hea<br />
 9 he only (12 total he - 3hea already counted)<br />
 6 ae only ( 9 total ae - 3hea already counted)<br />
 5 ha only ( 8 total ae - 3hea already counted)<br />
56 h  only (73 total h - (3hea + 9he + 5ha)counted)<br />
10 e  only (28 total e - (3hea + 9he + 6ae)counted)<br />
 7 a  only (21 total a - (3hea + 6ae + 5ha)counted)<br />
&#8212;-<br />
96 of 100 aliens with features. Four remain.</p>
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	<item>
		<title>By: mark</title>
		<link>http://www.tenproblems.com/20061116/problem-one-aliens/#comment-304</link>
		<dc:creator>mark</dc:creator>
		<pubDate>Sat, 18 Nov 2006 09:06:48 +0000</pubDate>
		<guid>http://www.tenproblems.com/20061116/problem-one-aliens/#comment-304</guid>
		<description>i think 4 is the answer.. using the venn diagram. but i think jason knows it.. difficult to explain.. ryt..</description>
		<content:encoded><![CDATA[<p>i think 4 is the answer.. using the venn diagram. but i think jason knows it.. difficult to explain.. ryt..</p>
]]></content:encoded>
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	<item>
		<title>By: Jason</title>
		<link>http://www.tenproblems.com/20061116/problem-one-aliens/#comment-302</link>
		<dc:creator>Jason</dc:creator>
		<pubDate>Fri, 17 Nov 2006 03:20:13 +0000</pubDate>
		<guid>http://www.tenproblems.com/20061116/problem-one-aliens/#comment-302</guid>
		<description>4 ?</description>
		<content:encoded><![CDATA[<p>4 ?</p>
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