The Guinness Encyclopedia

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Extensible Markup Language | 1995-08-15 | 5KB | 29 lines

<?xml version="1.0" encoding="utf-8" ?> <!DOCTYPE card PUBLIC "-//Apple, Inc.//DTD card V 2.0//EN" "" > <card> <id>44962</id> <filler1>0</filler1> <cantDelete> <false /> </cantDelete> <showPict> <true /> </showPict> <dontSearch> <false /> </dontSearch> <owner>5472</owner> <link rel="stylesheet" type="text/css" href="stylesheet_3106.css" /> <content> <layer>background</layer> <id>25</id> <text>ets and Paradoxes (7 of 7)VENN DIAGRAMS AND NUMERICAL DATAVenn diagrams can be used to assist with calculations that involve a subdivided population about which only fragmentary numerical data are available. The story of 'The Thirty-Sixth Man' provides an entertaining example . . .Vennseta is a spymaster. To his horror, he discovers that three hostile powers, Xylia, Yoravia and Zenobia, have cracked the cover of some of his agents. Unfortunately for Vennseta, the information he has is only fragmentary, but he has to find out which of his agents he can still trust.Of his 36 operatives, he knows that 21 have been cracked by Xylia, only 4 of whom have been cracked by no other power. He knows that 5 have been uncovered by Zenobia alone and that the cover of 12 has been broken by Xylia and Zenobia. Of those who are known to Yoravia, 9 are also known to Xylia and 7 are also known to Zenobia. His information tells him that 18 are entirely unsuspected by Yoravia.Wondering whether he has enough data, Vennseta draws one of those diagrams for which he is famed in the world of espionage. E is the set of all his espionage operatives. The circles he labels X, Y and Z, to represent the sets of agents cracked by, respectively, Xylia (X), Yoravia (Y) and Zenobia (Z). He then writes in the numbers to represent the data he has.He still has one piece of information that he cannot fit into his diagram, but he is quite sure it will be useful later.The spymaster decides he can now determine how many of his agents are known to all three powers, by considering the subdivisions of X. He adds the 4 who were cracked only by X, the 9 also cracked by Y and the 12 also cracked by Z. He gets a total of 25 agents cracked. But he sees that only 21 have been cracked by X, so there are, seemingly, 4 spies too many. He realizes what this means: 4 of the 9 + 12 must have been cracked by both Y and Z, as well as X. He decides to draw another diagram, putting this information into it.From his second diagram, he sees that 12 - 4 = 8 are not known to Y ; 9 - 4 = 5 are not known to Z ; and 7 - 4 = 3 are not known to X. The only subsets he has to determine are those agents known only to Y and those agents not known to any of the three hostile powers. He marks these sets by question marks.Vennseta puzzles a while, and then reaches for his one unused piece of information: 18 agents are unsuspected by Y. He quickly adds up the agents cracked by X and Z but out side Y: 5 + 8 + 4 = 17. This leaves one agent who is safe from all three powers.The spymaster is elated; not only have his diagrams, once again, solved his problem for him, but out there in hostile regions there is an agent on whom he can rely, absolutely. He idly scribbles in a 6 as the missing number in Y; he writes a large 1 in the rectangle outside the circles. Suddenly he stiffens and turns pale: how on earth can he find out which of his agents he can still trust?</text> </content> <content> <layer>background</layer> <id>23</id> <text>ΓÇó THE SCIENTIFIC METHODΓÇó CORRESPONDENCE, COUNTING AND INFINITYΓÇó COMPUTERSΓÇó LOGIC</text> </content> <content> <layer>background</layer> <id>36</id> <text>5868334494</text> </content> <name>p066-7</name> <script></script> </card>