document.write( "Question 900983: tom brought a notebook with 100 sheets and numbered its pages consecutively from 1 to 200. Jerry pulled out 43 sheets and added up all 86 page numbers written on both sides of each of the sheets. can the sum be equal to 2011? \n" ); document.write( "

Algebra.Com's Answer #546377 by Edwin McCravy(20055) $\"\"$ $\"About$

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Tom brought a notebook with 100 sheets and numbered its pages consecutively from
\n" ); document.write( "1 to 200. Jerry pulled out 43 sheets and added up all 86 page numbers written on
\n" ); document.write( "both sides of each of the sheets. can the sum be equal to 2011?
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document.write( "Every sheet has an odd number on the front and the next even number on the back.  \r\n" );
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document.write( "Let every front page have odd number  i=1,...,43\r\n" );
document.write( "and every back page have the next even number , i=1,...,43\r\n" );
document.write( "Thus the 43 sums of the numbers on the 43 pages, front and\r\n" );
document.write( "back, are , i=1,...43\r\n" );
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document.write( "We are investigating whether the sum of those 43 sums can be 2011.\r\n" );
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document.write( "Suppose \r\n" );
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document.write( "Divide both sides by 2\r\n" );
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document.write( "Thus we have reached a contradiction since we have\r\n" );
document.write( "an even number equalling to an odd number.\r\n" );
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document.write( "So we have shown that the sum cannot be 2011.\r\n" );
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document.write( "Edwin

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