document.write( "Question 464325: What is the sum of all the 4-digit numbers all of whose digits are odd?
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Algebra.Com's Answer #318084 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
What is the sum of all the 4-digit numbers all of whose digits are odd?
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document.write( "The other tutor's answer is incorrect.\r\n" );
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document.write( "There are 5 ways to choose each digit as 1,3,5,7,or 9,\r\n" );
document.write( "so the total number of 4 digit numbers with only odd\r\n" );
document.write( "digits is 5^4 or 625.  Think of all 625 numbers added \r\n" );
document.write( "up like this: \r\n" );
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document.write( " 1111\r\n" );
document.write( " 1113\r\n" );
document.write( " 1135\r\n" );
document.write( " ....\r\n" );
document.write( " ....\r\n" );
document.write( " 9995\r\n" );
document.write( " 9997\r\n" );
document.write( "+9999\r\n" );
document.write( "-----\r\n" );
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document.write( "Each of the 4 columns of 625 digits contains the\r\n" );
document.write( "same number of 1's as 3's as 5's as 7's and as 9's.  \r\n" );
document.write( "Therefore each of the 4 columns of 625 digits \r\n" );
document.write( "contains 125 1's, 125 3's, 125 5's, 125 7's, and 125 9's\r\n" );
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document.write( "So the sum of each column of digits is \r\n" );
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document.write( "125(1 + 3 + 5 + 7 + 9) = 125(25) = 3125\r\n" );
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document.write( "The column of thousands digits accounts for 3125000 toward the sum\r\n" );
document.write( "The column of  hundreds digits accounts for  312500 toward the sum\r\n" );
document.write( "The column of      tens digits accounts for   31250 toward the sum\r\n" );
document.write( "The column of      ones digits accounts for    3125 toward the sum\r\n" );
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document.write( "So the sum is is the sum of those numbers-> 3471875               \r\n" );
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document.write( "An easier way to do it is to realize it is the same as if all\r\n" );
document.write( "the digits were the average of the odd digits, which is 5. So\r\n" );
document.write( "the answer is the same as if every number among the 625 were \r\n" );
document.write( "replaced by 5555.  So 5555×625 = 3471875.\r\n" );
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document.write( "Edwin
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