document.write( "Question 1037482: The total number of subtractions that result in 11111 remaining after a four-digit number has been subtracted form a five-digit numer and the digits 1 through 9 have all been used is ______?\r
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\n" ); document.write( "\n" ); document.write( "PS. I was told that the answer is 24, but I don't really understand why... Thank you so much for helping! \n" ); document.write( "
Algebra.Com's Answer #655877 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Yes it's 24.  Here is why:\r\n" );
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document.write( "ABCDE\r\n" );
document.write( "-FGHI\r\n" );
document.write( "-----\r\n" );
document.write( "11111\r\n" );
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document.write( "It's clear that there can't be any \"borrowing\"\r\n" );
document.write( "in the subtraction.\r\n" );
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document.write( "It's clear that A can only be 1.  \r\n" );
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document.write( "So B-F = C-G = D-H = E-I = 1 and:\r\n" );
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document.write( "{(B,F),(C,G),(D,H),(E,I)} c {(3,2),(4,3),(5,4),(6,5),(7,6),(8,7),(9,8)}\r\n" );
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document.write( "We can't use (8,7) because then we'd have to use (6,5), and (4,3), but\r\n" );
document.write( "that wouldn't allow us to use 9 or 2.\r\n" );
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document.write( "So we can only use (9,8), (7,6), (5,4) and (3,2)  \r\n" );
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document.write( "Here is the smallest possibility:\r\n" );
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document.write( "13579\r\n" );
document.write( "-2468\r\n" );
document.write( "-----\r\n" );
document.write( "11111\r\n" );
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document.write( "There are 4!=24 ways to rearrange the last 4 \r\n" );
document.write( "columns that go after the first one. The\r\n" );
document.write( "first column can only be:\r\n" );
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document.write( "1\r\n" );
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document.write( "1\r\n" );
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document.write( "Then there are 4!=24 ways we can arrange these 4\r\n" );
document.write( "column after it:\r\n" );
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document.write( "3, 5, 7, 9\r\n" );
document.write( "2, 4, 6, 8\r\n" );
document.write( "-, -, -, -\r\n" );
document.write( "1, 1, 1, 1\r\n" );
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document.write( "Edwin

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