document.write( "Question 1043178: Mr. X has five objects, all having different weights from 1 through 5 kg. If he weights them three at a time, what is the largest possible number of different weights he can have? \n" ); document.write( "
Algebra.Com's Answer #658277 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "Since 5C3 is only 10, we will just list them all, \r\n" );
document.write( "add them and count the number of different sums \r\n" );
document.write( "of weights:\r\n" );
document.write( "\r\n" );
document.write( "1.  1+2+3 = 6\r\n" );
document.write( "2.  1+2+4 = 7\r\n" );
document.write( "3.  1+2+5 = 8\r\n" );
document.write( "4.  1+3+4 = 8\r\n" );
document.write( "5.  1+3+5 = 8\r\n" );
document.write( "6.  1+4+5 = 10\r\n" );
document.write( "7.  2+3+4 = 9\r\n" );
document.write( "9.  2+3+5 = 10\r\n" );
document.write( "9.  2+4+5 = 11\r\n" );
document.write( "10. 3+4+5 = 12\r\n" );
document.write( "\r\n" );
document.write( "So there are 7 different sums of weights, \r\n" );
document.write( "\r\n" );
document.write( "{6,7,8,9,10,11,12}\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );