document.write( "Question 1133243: Every positive integer can be expressed as a sum of distinct powers of 2.
\n" ); document.write( "Note that 1 and 2 are powers of 2. How many three-digit numbers are sums of
\n" ); document.write( "exactly 9 distinct powers of 2? \n" ); document.write( "
Algebra.Com's Answer #750430 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "The smallest possible sum of 10 (1 more than 9) distinct powers of 2 is\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We must omit 1 of those powers of 2 to get a sum of exactly 9 distinct ones.\r\n" );
document.write( "1023 is a 4-digit number.  To get the largest 3-digit number, 999, we must\r\n" );
document.write( "subtract 24 from 1023, and to get the smallest 3-digit number, 100, we must\r\n" );
document.write( "subtract 923 from 1023.\r\n" );
document.write( "\r\n" );
document.write( "So to get a 3-digit number from that sum, we must omit powers of 2 that\r\n" );
document.write( "are between 24 and 923.  The smallest power of 2 between those is 32, which\r\n" );
document.write( "is 25 and and the largest power of 2 between those is 512, which is 29. \r\n" );
document.write( "So there are 5 powers of 2 that we can omit from the sum of the first\r\n" );
document.write( "10 powers of 2, to get the sum of 9 powers of 2 that is a 3-digit number.  Answer: 5     \r\n" );
document.write( " \r\n" );
document.write( "Here are all 5 ways to omit a power of 2 from the sum of the smallest 10 powers\r\n" );
document.write( "of 2 that will give the sum of 9 powers of 2 that will be a 3-digit number: \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );