document.write( "Question 1172321: The integers 1, 2, 3, ...., 40 are written on white board. An operation is then repeated 39 times. In each repetition any two numbers say a and b currently on white board are erased and new number a + b -1 is written. What will be the number left on white board at the end? \n" ); document.write( "

Algebra.Com's Answer #797324 by Edwin McCravy(20056) $\"\"$ $\"About$

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The integers 1, 2, 3, ...., 40 are written on white board. An operation is then
\n" ); document.write( "repeated 39 times. In each repetition any two numbers say a and b currently on
\n" ); document.write( "white board are erased and new number a + b -1 is written. What will be the
\n" ); document.write( "number left on white board at the end?
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document.write( "The sum of the numbers on the board is 1+2+3+4+...+40 = 820\r\n" );
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document.write( "When I erase a and b, the sum of the 38 numbers on the board is 820-a-b.\r\n" );
document.write( "When I replace them with a+b-1, the sum of the 39 numbers on the board is\r\n" );
document.write( "820-a-b+a+b-1 or 819.\r\n" );
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document.write( "So the sum goes down 1 each time and so does the number of numbers on the board\r\n" );
document.write( "so when the operation is repeated the 40th time the sum of the numbers on the\r\n" );
document.write( "board will have gone down by 40 and the sum will be 820-40 or 780.\r\n" );
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document.write( "Ikleyn is right.  I got careless once I saw how to do it. It should have been\r\n" );
document.write( "820-39 = 781.  You can't do a 40th operation.  lol.  Happy Holidays! \r\n" );
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document.write( "Edwin

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