document.write( "Question 1204296: Find the sum of the digit of a 3 digit integers
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Algebra.Com's Answer #840473 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( " Attention to the visitor (and to the problem's creator)\r
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document.write( "    If you want to avoid misreading and misunderstanding, write \"three-digit integers\" \r\n" );
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document.write( "    instead of \"3 digit integers\", as this standard form is traditionally accepted in Math.\r\n" );
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document.write( "Three-digit integers are from 100 to 999. In all, there are 999 - 99 = 900 such integer numbers.\r\n" );
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document.write( "The ones digits are from 0 to 9.  \r\n" );
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document.write( "    Each ones digit from 0 to 9 is repeated with the same frequency;\r\n" );
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document.write( "    the number of different digits is 10 and the frequency of each digit is 900/10 = 90.\r\n" );
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document.write( "    So, the sum of all digits in the ones position is 90 times (1 + 2 + 3 + . . . + 9) =  = 5*9 = 45.\r\n" );
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document.write( "    90 times 45 is  90*45 = 4050.  Thus the sum of all 900 ones digits is 4050.\r\n" );
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document.write( "The tens digits are from 0 to 9.  \r\n" );
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document.write( "    Each tens digit from 0 to 9 is repeated with the same frequency;\r\n" );
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document.write( "    the number of different digits is 10 and the frequency of each digit is 900/10 = 90.\r\n" );
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document.write( "    So, the sum of all digits in the tens position is 90 times (1 + 2 + 3 + . . . + 9) =  = 5*9 = 45.\r\n" );
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document.write( "    90 times 45 is  90*45 = 4050.  Thus the sum of all 900 tens digits is 4050.\r\n" );
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document.write( "The hundreds digits are from 1 to 9.  \r\n" );
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document.write( "    Each hundreds digit from 1 to 9 is repeated with the same frequency;\r\n" );
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document.write( "    the number of different digits is 9 (the zero is not included) and the frequency of each digit is 900/9 = 100.\r\n" );
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document.write( "    So, the sum of all digits in the hundreds position is 100 times (1 + 2 + 3 + . . . + 9) =  = 5*9 = 45.\r\n" );
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document.write( "    100 times 45 is  100*45 = 4500.  Thus the sum of all 900 hundreds digits is 4500.\r\n" );
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document.write( "Now the ANSWER to the problem's question is this sum  4050 + 4050 + 4500 = 12600.\r\n" );
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\n" ); document.write( "\n" ); document.write( "In this problem, there is an underwater stone, so be CAREFUL:\r
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\n" ); document.write( "\n" ); document.write( " - the frequency of digits in the hundreds position (100)
\n" ); document.write( " is not the same as that in the tens and/or in the ones position (90).\r
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\n" ); document.write( "\n" ); document.write( "As I see from the post, the level of the problem's creator in Math is quite low, same as in English.\r
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