document.write( "Question 1030635: Your suitcase has 4-digit code lock. You forgot the code, but you do
\n" ); document.write( "remember that the sum of first two digits was equal to the sum of
\n" ); document.write( "two second digits. How many combinations do you need to check in
\n" ); document.write( "the worst possible scenario?
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #645499 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "There is 1 way the first two digits can sum to 0.  \r\n" );
document.write( "{00}\r\n" );
document.write( "There are 2 ways the first two digits can sum to 1.\r\n" );
document.write( "{01,10}\r\n" );
document.write( "There are 3 ways the first two digits can sum to 2.\r\n" );
document.write( "{02,11,20}\r\n" );
document.write( "There are 4 ways the first two digits can sum to 3.\r\n" );
document.write( "{03,12,21,30}\r\n" );
document.write( "There are 5 ways the first two digits can sum to 4.\r\n" );
document.write( "{04,13,22,31,40}\r\n" );
document.write( "There are 6 ways the first two digits can sum to 5.\r\n" );
document.write( "{05,14,23,32,41,50}\r\n" );
document.write( "There are 7 ways the first two digits can sum to 6.\r\n" );
document.write( "{06,15,24,33,42,51,60}\r\n" );
document.write( "There are 8 ways the first two digits can sum to 7.\r\n" );
document.write( "{07,16,25,34,43,52,61,70}\r\n" );
document.write( "There are 9 ways the first two digits can sum to 8.\r\n" );
document.write( "{08,17,26,35,44,53,62,71,80}\r\n" );
document.write( "There are 10 ways the first two digits can sum to 9.\r\n" );
document.write( "{09,18,27,36,45,54,63,72,81,90}\r\n" );
document.write( "There are 9 ways the first two digits can sum to 10.\r\n" );
document.write( "{19,28,37,46,55,64,73,82,91}\r\n" );
document.write( "There are 8 ways the first two digits can sum to 11.\r\n" );
document.write( "{29,38,47,56,65,74,83,92}\r\n" );
document.write( "There are 7 ways the first two digits can sum to 12.\r\n" );
document.write( "{39,48,57,66,75,84,93} \r\n" );
document.write( "There are 6 ways the first two digits can sum to 13.\r\n" );
document.write( "{49,58,67,76,85,94}\r\n" );
document.write( "There are 5 ways the first two digits can sum to 14.\r\n" );
document.write( "{59,68,77,86,95}\r\n" );
document.write( "There are 4 ways the first two digits can sum to 15.\r\n" );
document.write( "{69,78,87,96}\r\n" );
document.write( "There are 3 ways the first two digits can sum to 16.\r\n" );
document.write( "{79,88,97}\r\n" );
document.write( "There are 2 ways the first two digits can sum to 17.\r\n" );
document.write( "{89,98}\r\n" );
document.write( "There is 1 way the first two digits can sum to 18.\r\n" );
document.write( "{99}\r\n" );
document.write( "\r\n" );
document.write( "For each of those possible ways for the sum there are that same \r\n" );
document.write( "number of ways for the last two digits.  Therefore, the number\r\n" );
document.write( "of possible trials in the worst possible scenario, is the sum of \r\n" );
document.write( "the squares:\r\n" );
document.write( "\r\n" );
document.write( "1²+2²+3²+4²+5²+6²+7²+8²+9²+10²+9²+8²+7²+6²+5²+4²+3²+2²+1²\r\n" );
document.write( "\r\n" );
document.write( "The formula for the sum of the first n squares is n(n+1)(2n+1)/6\r\n" );
document.write( "\r\n" );
document.write( "So the sum of 1²+2²+3²+4²+5²+6²+7²+8²+9² = \r\n" );
document.write( "\r\n" );
document.write( "9(9+1)(2*9+1)/6 = 9(10)(19)/6 = 285\r\n" );
document.write( "\r\n" );
document.write( "And the sum 10²+9²+8²+7²+6²+5²+4²+3²+2²+1² is 10² or 100 more or 385\r\n" );
document.write( "\r\n" );
document.write( "Total 285+385 = 670\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );