document.write( "Question 1210183: In how many ways can we seat 3 pairs of siblings in a row of 10 chairs, so that nobody sits next to their sibling? (Two chairs will be left empty, of course.)
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Algebra.Com's Answer #851706 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The correct answer is 78960.  How do I know?  I wrote a program in LibertyBasic.\r\n" );
document.write( "I let A and B represent one pair of siblings, C and D represent another pair of\r\n" );
document.write( "siblings, and D and E represent another set of siblings. I let the X's refer to\r\n" );
document.write( "the 4 empty chairs.\r\n" );
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document.write( "My program ensures that A and B are never next to each other, that C and D are\r\n" );
document.write( "never next to each other, and that E and F are never next to each other. \r\n" );
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document.write( "The program I wrote also produces no duplications. For every new seating\r\n" );
document.write( "arrangement my program finds, my program always makes sure that it is NEVER\r\n" );
document.write( "identical to any one of the other arrangements it has found so far.  So all\r\n" );
document.write( "78960 arrangements my program found are definitely unique.\r\n" );
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document.write( "Except for the 4 X's for the empty chairs, the output shows all possible\r\n" );
document.write( "arrangements in alphabetical order.\r\n" );
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document.write( "Here are the first 10 of my output.\r\n" );
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document.write( "1             ACBDEXFXXX\r\n" );
document.write( "2             ACBDEXXFXX\r\n" );
document.write( "3             ACBDEXXXFX\r\n" );
document.write( "4             ACBDEXXXXF\r\n" );
document.write( "5             ACBDFXEXXX\r\n" );
document.write( "6             ACBDFXXEXX\r\n" );
document.write( "7             ACBDFXXXEX\r\n" );
document.write( "8             ACBDFXXXXE\r\n" );
document.write( "9             ACBDXEXFXX\r\n" );
document.write( "10            ACBDXEXXFX\r\n" );
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document.write( "Here are 10 where they changed from beginning with A to beginning with B.\r\n" );
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document.write( "8276          AXXXXFCEDB\r\n" );
document.write( "8277          AXXXXFDBCE\r\n" );
document.write( "8278          AXXXXFDBEC\r\n" );
document.write( "8279          AXXXXFDEBC\r\n" );
document.write( "8280          AXXXXFDECB\r\n" );
document.write( "8281          BCADEXFXXX\r\n" );
document.write( "8282          BCADEXXFXX\r\n" );
document.write( "8283          BCADEXXXFX\r\n" );
document.write( "8284          BCADEXXXXF\r\n" );
document.write( "8285          BCADFXEXXX\r\n" );
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document.write( "Here are 5 where they changed from beginning with DE to DF.\r\n" );
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document.write( "28169         DEXXXXFACB\r\n" );
document.write( "28170         DEXXXXFBCA\r\n" );
document.write( "28171         DFACBEXXXX\r\n" );
document.write( "28172         DFACBXEXXX\r\n" );
document.write( "28173         DFACBXXEXX\r\n" );
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document.write( "Here are 5 where they changed from beginning with XE to XF.\r\n" );
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document.write( "66679         XEXXXFDACB\r\n" );
document.write( "66680         XEXXXFDBCA\r\n" );
document.write( "66681         XFACBDEXXX\r\n" );
document.write( "66682         XFACBDXEXX\r\n" );
document.write( "66683         XFACBDXXEX\r\n" );
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document.write( "Now I'll skip on down to the final 10.\r\n" );
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document.write( "78951         XXXXFDACBE\r\n" );
document.write( "78952         XXXXFDACEB\r\n" );
document.write( "78953         XXXXFDAEBC\r\n" );
document.write( "78954         XXXXFDAECB\r\n" );
document.write( "78955         XXXXFDBCAE\r\n" );
document.write( "78956         XXXXFDBCEA\r\n" );
document.write( "78957         XXXXFDBEAC\r\n" );
document.write( "78958         XXXXFDBECA\r\n" );
document.write( "78959         XXXXFDEACB\r\n" );
document.write( "78960         XXXXFDEBCA\r\n" );
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document.write( "I can't post the entire output here, as it's too long. But you can see how the\r\n" );
document.write( "X's moved gradually from right to left.\r\n" );
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document.write( "78960 is the correct answer, with 3 pairs of siblings, and 4 empty chairs.\r\n" );
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document.write( "Edwin
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