\r\n" );
document.write( "Both the other two solutions are incorrect, according to the normal way \r\n" );
document.write( "circular-table enumeration problems are interpreted.\r\n" );
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document.write( "Ikleyn's answer of 36 would be correct if the table were assumed fixed \r\n" );
document.write( "so that it could not be rotated, then it would be the same as this \r\n" );
document.write( "unrotatable way, which is the way Ikleyn assumed the problem to be: \r\n" );
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document.write( "
\r\n" );
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document.write( "There would be 3!=6 ways to place the boys and 3! ways to place the girls.\r\n" );
document.write( "That would be (3!)(3!) = (6)(6) = 36 ways. Then Ikleyn's answer would \r\n" );
document.write( "have been correct, with this assumption, which is in line with reality.\r\n" );
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document.write( "However, the creators of circular table math problems always assume that the\r\n" );
document.write( "round table and the chairs are resting on a huge turntable and the huge\r\n" );
document.write( "turntable can be rotated in any of the positions below. So all of these 6\r\n" );
document.write( "seating positions below are considered by the problem creators to be just 1\r\n" );
document.write( "position, because the imaginary huge turntable can be rotated to form any one \r\n" );
document.write( "of them: \r\n" );
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document.write( "
\r\n" );
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document.write( "So we must divide the 36 ways by 6 and find that the solution intended by the\r\n" );
document.write( "creators of the problem is only 6 ways.\r\n" );
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document.write( "Even though I realize that circular tables in reality are NEVER placed on\r\n" );
document.write( "huge turntables, the people who make round-table math problems always\r\n" );
document.write( "assume it anyway. So we must always assume it when given a round-table \r\n" );
document.write( "problem, even though nobody puts tables and chairs on huge turntables.\r\n" );
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document.write( "The 6 ways are as follows. I will let P,Q, and R represent the three boys\r\n" );
document.write( "and X, Y, and Z represent the 3 girls. Then the 6 seating arrangements are\r\n" );
document.write( "these:\r\n" );
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document.write( "
\r\n" );
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document.write( "Any of the other 30 seating arrangements of Ikleyn's answer of 36, can be\r\n" );
document.write( "obtained by rotating the imaginary huge turntable on one of these 6. \r\n" );
document.write( "\r\n" );
document.write( "But the correct answer assumed by the creators is 6. (Although I agree with\r\n" );
document.write( "Ikleyn that the circular-table math problem creators are really the ones in\r\n" );
document.write( "error).\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" );
document.write( "![\"\"](\"/images/stars/stars-13.gif\")
