document.write( "Question 1101136: How many times do write digit 1 if you write all possible natural numbers up to seven digits using digits 0 and 1 only? \n" ); document.write( "
Algebra.Com's Answer #715732 by Edwin McCravy(20055)\"\" \"About 
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document.write( "If we consider having the non-natural number 0000000 along\r\n" );
document.write( "with the natural numbers in binary from 0000001 through 1111111, \r\n" );
document.write( "along with all the natural numbers in a list, like this:\r\n" );
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document.write( "0000000\r\n" );
document.write( "0000001\r\n" );
document.write( "0000010\r\n" );
document.write( "0000011\r\n" );
document.write( "0000100\r\n" );
document.write( "0000101\r\n" );
document.write( "0000110\r\n" );
document.write( "0000111\r\n" );
document.write( "...\r\n" );
document.write( "1111110\r\n" );
document.write( "1111111\r\n" );
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document.write( "Each column of digits in that list contains\r\n" );
document.write( "the same number of 1's as 0's\r\n" );
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document.write( "The last binary number in that list, 1111111, has decimal\r\n" );
document.write( "value\r\n" );
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document.write( "1(2^6)+1(2^5)+1(2^4)+1(2^3)+1(2^2)+1(2^1)+1(2^0) =\r\n" );
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document.write( "1(64)+1(32)+1(16)+1(8)+1(4)+1(2)+1(1) =\r\n" );
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document.write( "64+32+16+8+4+2+1 = 127, \r\n" );
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document.write( "so counting 0000000 there are 128 binary numbers in that list.\r\n" );
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document.write( "Each column of digits contains 128 digits, 64 or which \r\n" );
document.write( "are 0's and 64 of which are 1's.  Since there are 7 \r\n" );
document.write( "columns of digits, there are 7(64) = 448 0's and 448 1's.\r\n" );
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document.write( "Edwin
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