document.write( "Question 803357: If You Multiply 4321 By A Certain 4-digit Number, The 8-digit Answer You Get Ends In Its Reverse \n" ); document.write( "
Algebra.Com's Answer #484342 by Edwin McCravy(20060)\"\" \"About 
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If You Multiply 4321 By A Certain 4-digit Number, The 8-digit Answer You Get Ends In Its Reverse\r
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document.write( "In the multiplication below, the \"0\"'s\r\n" );
document.write( "are zeros, and the letter \"O\" is not\r\n" );
document.write( "used, and the small a,b,c are not the\r\n" );
document.write( "same as the capital letters A,B,C.\r\n" );
document.write( "\r\n" );
document.write( "      4321\r\n" );
document.write( "      ABCD\r\n" );
document.write( "     EFGHI\r\n" );
document.write( "    JKLMN0\r\n" );
document.write( "   PQRST00\r\n" );
document.write( "  UBWXY000\r\n" );
document.write( "  Zabc1234\r\n" );
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document.write( "We see that I=4, thus D=4 and\r\n" );
document.write( "EFGHI = 17284\r\n" );
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document.write( " \r\n" );
document.write( "      4321\r\n" );
document.write( "      ABC4\r\n" );
document.write( "     17284\r\n" );
document.write( "    JKLMN0\r\n" );
document.write( "   PQRST00\r\n" );
document.write( "  UBWXY000\r\n" );
document.write( "  Zabc1234\r\n" );
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document.write( "We see that N=C and N=5 so that\r\n" );
document.write( "8+5=13, so we put 5's for C and N,\r\n" );
document.write( "and remember that 1 is carried to\r\n" );
document.write( "the third column in the addition: \r\n" );
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document.write( "      4321\r\n" );
document.write( "      AB54\r\n" );
document.write( "     17284\r\n" );
document.write( "    JKLM50\r\n" );
document.write( "   PQRST00\r\n" );
document.write( "  UBWXY000\r\n" );
document.write( "  Zabc1234\r\n" );
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document.write( "Now we see that JKLM = 2160\r\n" );
document.write( "    \r\n" );
document.write( "      4321\r\n" );
document.write( "      AB54\r\n" );
document.write( "     17284\r\n" );
document.write( "    216050\r\n" );
document.write( "   PQRST00\r\n" );
document.write( "  UBWXY000\r\n" );
document.write( "  Zabc1234\r\n" );
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document.write( "Now since there was a 1 carried\r\n" );
document.write( "to the third column, T=9, and that\r\n" );
document.write( "makes B=9 as well, and we remember\r\n" );
document.write( "that a 1 is carried to the 4th\r\n" );
document.write( "column in the addition:\r\n" );
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document.write( "      4321\r\n" );
document.write( "      A954\r\n" );
document.write( "     17284\r\n" );
document.write( "    216050\r\n" );
document.write( "   PQRS900\r\n" );
document.write( "  UBWXY000\r\n" );
document.write( "  Zabc1234\r\n" );
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document.write( "Now we see that PQRS = 3888\r\n" );
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document.write( "      4321\r\n" );
document.write( "      A954\r\n" );
document.write( "     17284\r\n" );
document.write( "    216050\r\n" );
document.write( "   3888900\r\n" );
document.write( "  UBWXY000\r\n" );
document.write( "  Zabc1234\r\n" );
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document.write( "If we remember that ther was a 1\r\n" );
document.write( "carried to the 4th column then when\r\n" );
document.write( "we add 1+7+6+8+Y to get a number\r\n" );
document.write( "ending in 1, Y must be 9 so that\r\n" );
document.write( "1+7+6+8+9=31, with 3 to carry to the\r\n" );
document.write( "5th column.  And so A=9\r\n" );
document.write( "\r\n" );
document.write( "      4321\r\n" );
document.write( "      9954\r\n" );
document.write( "     17284\r\n" );
document.write( "    216050\r\n" );
document.write( "   3888900\r\n" );
document.write( "  UBWX9000\r\n" );
document.write( "  Zabc1234\r\n" );
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document.write( "Now we have the answer, 9954, but\r\n" );
document.write( "here are the rest of the digits:\r\n" );
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document.write( "      4321\r\n" );
document.write( "      9954\r\n" );
document.write( "     17284\r\n" );
document.write( "    216050\r\n" );
document.write( "   3888900\r\n" );
document.write( "  38889900\r\n" );
document.write( "  43011234\r\n" );
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document.write( "Edwin
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