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July 2018 little math problem
07-29-2018, 01:02 PM
Post: #24
RE: July 2018 little math problem
(07-28-2018 01:15 PM)Albert Chan Wrote:  Mini-Challenge:

(*) 2 symmetries does not overlap for sides = 4, 6, 8, 10, 12, 14, ... Why ?

In other words, for even sided zigzag, we can indeed reduce primary solutions in half.

You do not need a calculator to prove this ...

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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Messages In This Thread
July 2018 little math problem - pier4r - 07-25-2018, 08:52 PM
RE: July 2018 little math problem - DavidM - 07-26-2018, 04:03 AM
RE: July 2018 little math problem - DavidM - 07-26-2018, 03:38 PM
RE: July 2018 little math problem - pier4r - 07-26-2018, 12:36 PM
RE: July 2018 little math problem - pier4r - 07-27-2018, 10:03 AM
RE: July 2018 little math problem - DavidM - 07-28-2018, 04:22 PM
RE: July 2018 little math problem - Albert Chan - 07-29-2018 01:02 PM
RE: July 2018 little math problem - pier4r - 08-01-2018, 02:13 PM



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