document.write( "Question 1188391: Peter and Paul are playing a game involving 60 plastic sticks that are on the table between them. On a turn, a player may remove up to from 1 to 7 sticks from said table. The player that removes the last stick wins. Peter can't guarantee that he'll win the game unless he goes first and removes \"k\" sticks. The value of \"k\" is?\r
\n" ); document.write( "\n" ); document.write( "a) 1 b) 2 c) 4 d) 6 e) 7 \n" ); document.write( "
Algebra.Com's Answer #819475 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "Peter's object is to leave Paul with 8 sticks the last time.  Because Paul\r\n" );
document.write( "can't then pick them all up.  So regardless of how many Paul removes, Peter\r\n" );
document.write( "will be able to remove the rest, for there will be 7 or less.\r\n" );
document.write( "\r\n" );
document.write( "So to leave Paul with 8 the last time Peter must have left him with 16\r\n" );
document.write( "before that. For instance, if Pau1 removes 1, leaving Peter with 15, Peter will\r\n" );
document.write( "then remove 7 and leave Paul with 8.  Or, say, if Pau1 picks up 7, leaving Peter\r\n" );
document.write( "with 9, Peter will then pick up 1, leaving Paul with 8. \r\n" );
document.write( "\r\n" );
document.write( "So to win, Peter must leave Paul with a multiple of 8 each time.  Peter can\r\n" );
document.write( "always do that if he starts first.  Beginning with 60 sticks, Peter must leave\r\n" );
document.write( "Paul with 56, the largest multiple of 8 not exceeding 60.  So Peter must begin\r\n" );
document.write( "by first removing k=4 sticks, to leave Paul with 56.\r\n" );
document.write( "\r\n" );
document.write( "[BTW, if Paul starts first, and doesn't know the trick, then if Paul at any time\r\n" );
document.write( "leaves Peter with anything other than a multiple of 8, Peter can then win\r\n" );
document.write( "because all he has to do is remove enough to leave Paul with a multiple of 8.]\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );