document.write( "Question 1164387: I already know the answer to this problem, but I need a better explanation as to how to get the answer, like a step-by-step kind of way.\r
\n" ); document.write( "\n" ); document.write( "Three circular cardboard disks have numbers written on the front and back sides.
\n" ); document.write( "The number written on the front of Disk 1: 6
\n" ); document.write( "The number written on the front of Disk 2: 7
\n" ); document.write( "The number written on the front of Disk 3: 8\r
\n" ); document.write( "\n" ); document.write( "By tossing all three disks and adding the numbers that show face up, we can obtain these totals: 15, 16, 17, 18, 19, 20, 21, and 22. What numbers are written on the back sides of these disks? \n" ); document.write( "
Algebra.Com's Answer #788815 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "I'd rather reason something out all by myself when possible, rather than\r\n" );
document.write( "go looking where someone else has already figured it out.  That's just me.\r\n" );
document.write( "Being able to reason it out yourself is the main thing, not to know the\r\n" );
document.write( "answer.  This student already knew the answer.  Trying to do it yourself is\r\n" );
document.write( "the only way to train your brain.  When I studied math in school and\r\n" );
document.write( "college, I would cover up the explanation in the book of how to solve each\r\n" );
document.write( "problem, and first try to figure it out all by myself.  Then only when I got\r\n" );
document.write( "stuck,  would I uncover the explanation.  Then I'd only uncover a little at\r\n" );
document.write( "a time.   \r\n" );
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document.write( "Suppose the back side numbers are A, B and C, like this:\r\n" );
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document.write( "Disk   Front    Back\r\n" );
document.write( "  1      6       A\r\n" );
document.write( "  2      7       B\r\n" );
document.write( "  3      8       C\r\n" );
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document.write( "One thing to notice is that there are exactly 2 ways each disk can land,\r\n" );
document.write( "so there are 2∙2∙2=8 ways they can all three land.  And there are 8 numbers\r\n" );
document.write( "15, 16, 17, 18, 19, 20, 21, and 22 numbers they must add to, so there are no\r\n" );
document.write( "\"extras\", that is, there is only one way to get each of those sums. \r\n" );
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document.write( "If the first two disks fall 6 and 7, there must be a 9 on the back of the\r\n" );
document.write( "third disk so that the largest sum, 6+7+9=22, can be made.  So C=9.\r\n" );
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document.write( "If the first and third disks fall 6 and 8, there must be a 2 on the back of\r\n" );
document.write( "the second disk so that the smallest sum, 6+8+2=16 can be made.  So B=2.\r\n" );
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document.write( "We can now make these sums:\r\n" );
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document.write( "2+7+8=17, 2+7+9=18, 6+7+8=21, 6+7+9=22 \r\n" );
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document.write( "If the second and third disks fall 7 and 8, there must be a 5 on the back of\r\n" );
document.write( "the first disk so that the largest remaining sum 6+5+9=20 can be made.  So\r\n" );
document.write( "A=5.\r\n" );
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document.write( "Now we must check to see if we can make all the sums:\r\n" );
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document.write( "Disk   Front    Back\r\n" );
document.write( "  1      6       2\r\n" );
document.write( "  2      7       5\r\n" );
document.write( "  3      8       9\r\n" );
document.write( "       \r\n" );
document.write( "2+5+8=15, 2+5+9=16, 2+7+8=17, 2+7+9=18, 6+5+8=19, 6+5+9=20, 6+7+8=21, \r\n" );
document.write( "6+7+9=22.\r\n" );
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document.write( "Ah, sweet success!\r\n" );
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document.write( "Edwin
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