document.write( "Question 1050045: The explorer said the 2 numbers she added used each digit 1-8 only once - the answer is 7785. What two numbers are added?\r
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Algebra.Com's Answer #665635 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( " ABCD\r\n" );
document.write( "+EFGH\r\n" );
document.write( " 7785\r\n" );
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document.write( "The first two digits of 7785 are 7's.\r\n" );
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document.write( "Since we can't use 9, the largest sum of two digits\r\n" );
document.write( "is 8+7 which is 15, which ends in 5.  So there is\r\n" );
document.write( "no way to get the two 7's in the beginning of the\r\n" );
document.write( "7785, by carrying 1 from the preceding column, so\r\n" );
document.write( "there can be no carrying to the first two columns.\r\n" );
document.write( "So A+E=7 and B+F=7\r\n" );
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document.write( "The only pairs of digits that add to 7 are these three\r\n" );
document.write( "1+6, 2+5, and 3+4.\r\n" );
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document.write( "The third digit is 8, which is just 1 more than 7.\r\n" );
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document.write( "That suggests that there was 1 to carry after\r\n" );
document.write( "adding D+H and getting 15.\r\n" );
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document.write( "The only digits that aren't used in the three pairs \r\n" );
document.write( "of digits that have sum 7 are the digits 7 and 8.  \r\n" );
document.write( "We notice that they have sum 15.\r\n" );
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document.write( "So we put the 7 and 8 on the right end, then there\r\n" );
document.write( "is 1 to carry to the third column.\r\n" );
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document.write( "   1\r\n" );
document.write( " ABC7\r\n" );
document.write( "+EFG8\r\n" );
document.write( " 7785\r\n" );
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document.write( "Now all that's left is to use those three pairs of\r\n" );
document.write( "digits to fill in the other three pairs of digits.\r\n" );
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document.write( "There are lots of ways to arrange those three pairs\r\n" );
document.write( "of digits that have sum 7.  \r\n" );
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document.write( "We can pick A+E=7 to be 1+6\r\n" );
document.write( "Then pick B+F=7 to be 2+5\r\n" );
document.write( "Finally C+G=7 would be 3+4\r\n" );
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document.write( "So one answer is\r\n" );
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document.write( "   1\r\n" );
document.write( " 1237\r\n" );
document.write( "+6548\r\n" );
document.write( " 7785\r\n" );
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document.write( "You can swap these around any way you like,\r\n" );
document.write( "but there will always be a 7 and 8 on the\r\n" );
document.write( "right end, and the other three columns\r\n" );
document.write( "will be the only three possible ways to get 7. \r\n" );
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document.write( "For a couple of examples, you can arrange them \r\n" );
document.write( "these ways:\r\n" );
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document.write( "   1         1 \r\n" );
document.write( " 4657      5368              \r\n" );
document.write( "+3128     +2417 \r\n" );
document.write( " 7785      7785\r\n" );
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document.write( "or any of many other ways.  There are, in fact,\r\n" );
document.write( "96 different ways to arrange the digits!  That\r\n" );
document.write( "is a combinatorial problem which you will\r\n" );
document.write( "eventually study if you take enough mathematics.\r\n" );
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document.write( "Yes I know, TMI, :)\r\n" );
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document.write( "Edwin
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