July 2018 little math problem
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07-29-2018, 01:02 PM
Post: #24
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RE: July 2018 little math problem
(07-28-2018 01:15 PM)Albert Chan Wrote: Mini-Challenge: The problem of complement symmetry was its overlap with reversing digits symmetry. This led to its inability to generate unique symmetrical solutions. Prove by contradiction: To follow the notation of the 4-sided zigzag, let e be middle number of an even-sided zigzag. Let's shift the numbers, so available digits = -side to side Assume 2 symmetries overlap, middle zigzag look like this: (c d e f g) => (c d 0 -d -c) For the center, sum = 0, e = 0, we have: (c d e f g) => (c -c 0 f -f) so, for both equation g = -c = -f, or c = f But, all numbers must be different, assumption was wrong => 2 symmetries have no overlap. For even-sided zigzag, we can cut primary solutions in half. QED |
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