document.write( "Question 1183662: Suppose there are 40 students in a class. Is there a month in the year in which at least 4 students were born? \n" ); document.write( "
Algebra.Com's Answer #814080 by ikleyn(52906) You can put this solution on YOUR website! .\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "As it is worded, printed, posted and presented, this formulation is INCORRECT and is good for re-cycling, ONLY.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "The correct formulation is as follows:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " Suppose there are 40 students in a class. Prove that \n" ); document.write( " there is a month in the year in which at least 4 students were born.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "The solution is in couple of lines.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \r\n" ); document.write( " If we assume, in opposite, that the number of birthdays is no more than 3 in each of 12 months of the year,\r\n" ); document.write( "\r\n" ); document.write( " then the total number of students in the class is no more than 3*12 = 36.\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( " It contradicts to the given part that the number of students in the class is 40.\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( " The contradiction proves the statement.\r\n" ); document.write( "\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |