16
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Please explain the following math.
To start, here are some basic relationships - creative thinking may help (or not)

1) p < c < h < n1 <= n2

The pipe symbol is used as shorthand for ROTATE NEXT VALUE 90 DEGREES or 2 pipes to rotate the variable's value by 180 degrees, etc (although no more than 2 pipes are needed)

2) a = ||c
3) n1 = ||n2

A number can be multiplied by a variable's "value" to adjust the variable's value– but addition or subtraction like a-2 is not permitted

4) 2a = u; u = 2a
5) d = 2h

Division is permitted in certain cases; these are similar to fractions. In fact, they must be written as such! Pipe-rotation is permitted in either the numerator or denominator.

6) s = p / c
7) e = |h / p

This is not traditional math. So this simple line may be a good place to start. The following reduces to o rather than 1:

8) p/p = o

Some variables come in pairs [b1 b2] but not ranges like b1 - bn or other one-to-many relationships

9) b1, b2 = h/|h/h

Here are a few final examples… please explain all 12.
No complicated math or knowledge is required and there are additional hidden clues throughout to ensure this is solvable without a computer (but there is no {no-computers} tag in case you feel it is helpful?)
Additional note - basic knowledge of English is useful.

10) l = 3p
11) n1 <> r1 = ||r2
12) q = n2/|h/p

Hint:

< > signs represent size comparisons.
Equal signs represent approximate equality, 2 being the most suspect; a=c might also be a good approximation. Fortunately the path to solve involves more than the numbered equations.

Hint 2:

Hmmm, each blockquote is preceded by a block of rambling text. Suspicious.

Hint 3:

Combine the keyword in the title with the tags and knowledge in a logical way.

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  • $\begingroup$ Which of the twelve relationships would you suggest to be the best inroad into this puzzle? $\endgroup$ Nov 29 '21 at 11:16
  • 1
    $\begingroup$ @sarsaparilla It may help to treat this as enigmatic; there is more going on than meets the eye. The title and area around "a good place to start" is a good place to start. $\endgroup$
    – Amoz
    Nov 29 '21 at 15:00
11
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I think each letter represents

A punctuation mark

Where the clever thing going on here is

We must watch for where they appear in the text

With the following correspondences

a = '
b1, b2 = [, ]
c = ,
d = – (dash, roughly twice a hyphen)
e = !
h = - (hyphen)
l = ...
n1, n2 = (, )
o = :
p = .
q = ?
r1, r2 = {,}
​ ​ u = "

Further information about the equations

Whenever we see a division symbol, this represents that we put one symbol over the other, so a semicolon is a period over a comma, and a colon is a period over a period. You have to use your imagination a little as, for example, a ? is represented by a right bracket over a vertical line over a period.

The really clever thing going on here is that if we read the paragraph before each equation, we see the punctuation marks appearing in the exact order that they appear in the equations. This is what determines the ordering. In the first paragraph, for example, the period appears before the comma which is before the hyphen which is before the pair of brackets (considered part of a unit) and so we have
p < c < h < n1 <= n2

Title

Notice that all of these punctuation marks represent pauses (interruptions) in grammar.

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  • $\begingroup$ Great solve! You may have misread the equation for q: ) / |- / . $\endgroup$
    – Amoz
    Dec 13 '21 at 17:00
  • $\begingroup$ @Amoz Yes, I did, thanks. Great question! $\endgroup$
    – hexomino
    Dec 13 '21 at 17:23

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