document.write( "Question 1096948: What's the sum of all the three-digits numbers I can form from digits 0-9 if
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Algebra.Com's Answer #711398 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
The above is incorrect. Sorry, Jorrell.
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document.write( "If the hundreds digits could be 0's, the problem would be much\r\n" );
document.write( "easier.  So let's begin by pretending that the hundreds digits\r\n" );
document.write( "can be 0, and finding that sum first.  Then we will find the\r\n" );
document.write( "sum of those with 0's as the hundreds digit, and subtract.\r\n" );
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document.write( "Suppose we had them all listed to add like this:\r\n" );
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document.write( " 012\r\n" );
document.write( " 013\r\n" );
document.write( " 014\r\n" );
document.write( " ...\r\n" );
document.write( " ...\r\n" );
document.write( " 098\r\n" );
document.write( " 102\r\n" );
document.write( " 103\r\n" );
document.write( " ...\r\n" );
document.write( " ...\r\n" );
document.write( " ...\r\n" );
document.write( " 986\r\n" );
document.write( "+987\r\n" );
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document.write( " sum\r\n" );
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document.write( "There are 10*9*8 = 720 numbers in that list.  There are an\r\n" );
document.write( "equal number of each digit in each column, so there are 720/10\r\n" );
document.write( "or 72 of each digit in each column.  Since the sum of the digits\r\n" );
document.write( "0+1+2+3+4+5+6+7+8+9 = 45, the sum of each of the three columns\r\n" );
document.write( "of digits is 45*72 = 3240.\r\n" );
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document.write( "The hundreds column will contribute 324000 toward the sum, the \r\n" );
document.write( "tens column will contribute 32400, and the ones column will \r\n" );
document.write( "contribute 3240, so the sum is 324000+32400+3240 = 359640.  That \r\n" );
document.write( "would be the answer if 0 could be used as the hundreds digit of \r\n" );
document.write( "a 3 digit number.  But alas, it cannot!  :)\r\n" );
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document.write( "So now we calculate how much we must subtract from the 359640.\r\n" );
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document.write( "We must now find the sum of this list:\r\n" );
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document.write( " 012\r\n" );
document.write( " 013\r\n" );
document.write( " 014\r\n" );
document.write( " ...\r\n" );
document.write( " ...\r\n" );
document.write( " 098\r\n" );
document.write( "----\r\n" );
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document.write( "Since the hundreds digits are all 0's there are no 0's in the\r\n" );
document.write( "tens or ones digit columns.  So there are 9*8 = 72 numbers in \r\n" );
document.write( "that list.  There are an equal number of each digit, 1 though\r\n" );
document.write( "9 in each of the tens and ones columns, so there are 72/9 or \r\n" );
document.write( "8 of each digit 1 thru 9 in the tens and ones columns.  Since \r\n" );
document.write( "the sum of the 9 digits 1+2+3+4+5+6+7+8+9 = 45, \r\n" );
document.write( "the sum of each of the two columns of digits is 45*8 = 360.  \r\n" );
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document.write( "The tens column will contribute 3600 toward the sum, and the \r\n" );
document.write( "ones column will contribute 360, so the sum is 3600+360 = 3960.  \r\n" );
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document.write( "So we subtract that from 359640.\r\n" );
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document.write( "Answer = 359640-3960 = 355680\r\n" );
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document.write( "Edwin
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