document.write( "Question 581368: How many four-digit integers between 5000 and 6000 are there for which the
\n" ); document.write( "thousands digit equals the sum of the other three digits? \n" ); document.write( "
Algebra.Com's Answer #371606 by Edwin McCravy(20064)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "\r\n" );
document.write( "Since the first digit is 5, the other three digits must sum to 5\r\n" );
document.write( "\r\n" );
document.write( "If the second digit is 0 the other two digits must sum to 5, so they\r\n" );
document.write( "are 0+5, 1+4, or 2+3 or their reverses 5+0, 4+1, amd 3+2, that 6\r\n" );
document.write( "\r\n" );
document.write( "If the second digit is 1, the last two digits must sum to 4, so they\r\n" );
document.write( "are 0+4, 1+3, or 2+2.  The first two have reverses, so that's 5 more\r\n" );
document.write( "\r\n" );
document.write( "If the second digit is 2, the last two digits must sum to 3, so they\r\n" );
document.write( "are 0+3 and 1+2, and their reverses, so that's 4 more.\r\n" );
document.write( "\r\n" );
document.write( "If the second digit is 3, the last two digits must sum to 2, so they\r\n" );
document.write( "are 0+2 and 1+1 and the reverse of the first, so that's 3 more.\r\n" );
document.write( "\r\n" );
document.write( "If the second digit is 4, the last two digits must sum to 1, so they\r\n" );
document.write( "are 0+1 and its reverse, so that's 2 more\r\n" );
document.write( "\r\n" );
document.write( "If the second digit is 5, the last two digits must sum to 0, so they\r\n" );
document.write( "are 0+0, so that's 1 more.\r\n" );
document.write( "\r\n" );
document.write( "Total = 6+5+4+3+2+1 = 21.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " 1.  5005\r\n" );
document.write( " 2.  5014\r\n" );
document.write( " 3.  5023\r\n" );
document.write( " 4.  5032\r\n" );
document.write( " 5.  5041\r\n" );
document.write( " 6.  5050\r\n" );
document.write( " 7.  5104\r\n" );
document.write( " 8.  5113\r\n" );
document.write( " 9.  5122\r\n" );
document.write( "10.  5131\r\n" );
document.write( "11.  5140\r\n" );
document.write( "12.  5203\r\n" );
document.write( "13.  5212\r\n" );
document.write( "14.  5221\r\n" );
document.write( "15.  5230\r\n" );
document.write( "16.  5302\r\n" );
document.write( "17.  5311\r\n" );
document.write( "18.  5320\r\n" );
document.write( "19.  5401\r\n" );
document.write( "20.  5410\r\n" );
document.write( "21.  5500\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );