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using only addition and subtraction signs, and the given order, make this equation true:

1( )2( )3( )4( )5( )6( )7( )8( )9( )0=10

2007-09-09 11:00:41 · 1 answers · asked by cook c 3 in Science & Mathematics Mathematics

1 answers

1( )2( )3( )4( )5( )6( )7( )8( )9( )0=10
where ( ) is either addition and subtraction sign, does not have a solution.
Prof: Let every ( ) to be "+" first, the sum (1+2+3+...+9) is 45. Suppose we change the "+" sign to a "-" sign in front of a number n, where 0<= n <= 9, the sum would be reduced by 2n.
Hence, no matter how many "+" signs would be changed to the "-" signs, the change in the sum would be always even.
To achieve the result 10 by change some "+" sins to "-" signs in the original summation with sum 45, the change in the sum must be odd: 45 - 10 = 35. Therefore, this problem does not have a solution at all.

2007-09-09 11:15:21 · answer #1 · answered by Hahaha 7 · 0 0

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