William

At the end of the video, there is a most surprising conclusion. Worth a knowing chuckle!

We agree that, using normal nomenclature:
P-Q/2=n!. . . .(1)
P/2 -Q/2 = n. . . (2)
From which:
P=2(n!-n) . . .. (3) and
Q=2(n!-2n). . . (4)

You have tabulated several values of P and Q derived using those equations..

You have gone on to show that in each example, the end result is what you expected.

Let's look at it another way.
P-Q/2 = 2(n!-n) -2(n!-2n)/2 = 2n!-2n-n!+2n = n!
and
P/2-Q/2 = 2(n!-n)/2 -2(n!-2n)/2 = n!-n -n! +2n = n

Great result, except that is where you started from. You have merely proved your arithmetic has been faultless, so the results are not interesting!

If n = an integer value of x, and if there are no exceptions to the process, the two results for (1) and (2) are always x! and x, respectively.

E&OE

This is quite irrelevant.

The clear intention of the original designer of the problem (I assume not the OP in this forum) was for readers who obeyed the standard process ("*/" then "+-") to evaluate the LHS, and be initially shocked by the statement that it was equal to a clearly incorrect number, not noticing the  "meta" addition of the factorial indicator. That is why I referred to the problem as being somewhat of a philosophical problem, a hybrid of text and maths.

I would like to introduce an analogy.
The adept mathematician understands how f', f'' etc. are used to represent dy/dx, d2y/d2x (you know what I mean- I don't know how to show superscript in this forum). This is an accepted shorthand, and no one would adapt or modify it. It has a meaning, which is universally understood.

I think, in the same way, the standard notation implies a process which is universally understood, where that notation is used. So if I write an expression using that notation, that is what I intend. If I meant to evaluate a "+-" function before a "*/" function, I would parse the expression in accordance.

The expansion of the expression in its correct and incorrect  formats may be interesting; a quick glance at the working shows interesting relationships - but it is an ephemera, a castle built on clay. It has nothing to do with the clever joke implied by the original maths expression in its text matrix.

So if one generalizes that so that evaluated the right way gives an answer that is factorial of the answer evaluated the wrong way, one gets two simultaneous equations.

For answers of 5 factorial and 5 the values of p and q are 230 and 220 respectively.

Solving the two simultaneous equations so as to provide results for p and for q for a given value of n, gives the following.

p=2(n! - n)

q= 2(n! - 2n)

So, if n=1, p=0 and q=-2,

so the equation is

0 - (-2 x 0.5) = 1!

(0 - -2) x 0.5 = 1

If n=2, then p = 0 and q=-4

0 - (-4 x 0.5) = 2!

(0 - -4) x 0.5 = 2

If n=3, then p=6 and q = 0

6 - (0 x 0.5) = 3!

(6 - 0) x 0.5 = 3

If n=7, then p = 10066 and q = 10052

10066 - (10052 x 0.5) = 7!

(10066 - 10052) x 0.5 -= 7

William

(p - q) x 0.5 = y

This is not called up by the original expression, and is a misreading of the convention. Effectively, you have introduced it as a red herring. Of course, the rhs in the given expression would become:
(230-220)/2 = 5.
This solution is a non-starter, except for an eccentric.

The accepted general convention is as the second:

,
so the rhs becomes:
230 - (220/2) = 230-110 = 120, which is 5!

p.s. As this is a "nice" forum, it might be y's to mind our p's and q's!

(p - q) x 0.5 = n

and

p - (q x 0.5) = n!

Then given n, what are the values of p and q?

William

I got quite indignant at first, until I noticed the twist. Very clever, bringing the mathematically knowledgeable down a peg.

Interesting philosophical point here, mixing maths and text!

Harking back to my schooldays, you always do the multiplication or division sum first BEFORE attempting the addition or subtraction unless brackets are used, in which case the bit inside the bracket is calculated first, am I right? All of which would mean the answer is 5! or 120.

Why did I get mixed up in all of this?

My simplistic way of seeing the "problem" is that the answer is five. Why dos he say that we will not believe it? Unless you do the right hand side of the equation fist, then the answer becomes 230-110=120.

But most people in the western world read from left to right.

It seems that you’ve forgotten your lesson about factorials, Albert!!

Unless you do the right hand side of the equation first, then the answer becomes 230-110=120.

Which is correct = 5!, as Mr Cheetham says. Jack will explain. Perhaps Mr C should end his sentences with a full stop.

But most people in the western world read from left to right.