Given this equation,  0= 1__ 2__3__4__5 The blanks represent + or - only.  I know that there is not a solution, my question is... is there a mathematical rule or reasoning as to why it's true. In other words, how can I explain this to someone without going through all 16 combinations with them?

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.6: Permutations
Problem 37E
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Given this equation, 

0= 1__ 2__3__4__5

The blanks represent + or - only. 

I know that there is not a solution, my question is... is there a mathematical rule or reasoning as to why it's true. In other words, how can I explain this to someone without going through all 16 combinations with them?

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