What, the answer isn't the No of the Yes is?

Question

Doorknob knows exactly how to solve this, so I ask him to not answer this question.

Well, here's the puzzle:

No, an answer is the cube without A, No?
The Yes is No.
The squared answer, Yes, is to an answer.
A Yes without the Yes is to the answer.
Yes, the answer is No.
Yes, the answer to a no is 432.
What is the answer?

And That's it ... Now for some hints

I tried my best to make it as grammatically correct as I could, but nope, too hard.
I'm not gonna put any tags on because the key thing to this puzzle is that you need to figure out what type of puzzle it is. Maybe after it gets answered.
Just that the 4th sentence says the answer is No does not mean that the answer is no.

A few more things

I'm being serious here; it works perfectly. If you get it, it's gonna be a EUREKA!!! moment because it works perfectly.
I have added a tag because it is obvious that rand al'thor is on the right track. Probably post the answer in 3 weeks (if not flagged for unclear puzzle).
Someone managed to solve an earlier version of this (same concept) and a bunch of people here are a lot better at solving than him so... I don't think its terribly hard...
If you don't get the answer I'm looking for, but manage to make a reasonable answer, I will give you an upvote, but not an answer mark.
This puzzle was inspired by a conversation with Doorknob and someone else (not on this site).

Answer 1

The EUREKA moment is to realise that

some of the words (yes, no, a, the, answer?) represent numbers or mathematical operations.

E.g.

'is' means = and 'without' means -.

Let

Y, N, A, a, t, T denote 'Yes', 'No', 'answer', 'a'/'an', 'to', 'the' respectively.

(I don't know whether the capitalisation in some 'Yes's and 'No's is relevant.) We have

No, an answer is the cube without A, No?
The Yes is No.
The squared answer, Yes, is to an answer.
A Yes without the Yes is to the answer.
Yes, the answer is No.
Yes, the answer to a no is 432.
What is the answer?

These statements become:

(1) No, an answer is the cube without A, No?

$N a A = T^3 - a N$

(2) The Yes is No.

$T Y = N$

(3) The squared answer, Yes, is to an answer.

$T^2 A Y = t a N$

(4) A Yes without the Yes is to the answer.

$a Y - T Y = t T A$

(5) Yes, the answer is No.

$Y T A = N$

(6) Yes, the answer to a no is 432.

$Y T A t a N = 432$

Note that (6) implies

none of our six variables can be zero. This will help with cancellation later!

Big spoiler block now with a lot of algebra.

By (2) and (5), $A=1$. Substitute in $A=1$ and $N=TY$ to get:
$(1)\Rightarrow Na=T^3-aN \Rightarrow 2TYa=T^3 \Rightarrow T^2=2aY$.
$(3)\Rightarrow T^2Y=taTY \Rightarrow T=ta$.
$(4)\Rightarrow aY-TY=tT=t^2a.$
$(6)\Rightarrow YTtaTY=432 \Rightarrow Y^2(ta)^2ta=432 \Rightarrow (Y=4, T=3)$.

So 'the answer' is

$TA =$ 3.

Answer 2

Following rand and reading this as a

set of simultaneous equations,

and ignoring

capitalisation and punctuation

because

the hint about grammatical correctness suggests that capitalisation and punctuation are here concerns of presentation only,

try the substitutions

"no" $\rightarrow$ N
"an", "a" $\rightarrow$ 1
"answer" $\rightarrow$ S
"is" $\rightarrow$ =
"the" $\rightarrow$ 3
"cube", "cubed" $\rightarrow$ ^3
"without" $\rightarrow$ - (minus)
"yes" $\rightarrow$ Y
"to" $\rightarrow$ 2

We get

N S = 27 - A N
3 Y = N
27 S Y = 2 S
A Y - 3 Y = 2 3 S
Y 3 S = N
Y 3 S 2 N = 432,

i.e.

NS = 27 - AN
3Y = N
27 Y = 2 (unless S=0)
Y(A-3) = 6S
3YS = N
6 YSN = 432 => YSN = 72 (so S can't be 0)

which unfortunately

is a set of equations without a solution

Might a eureka moment with the "little is large" hint straighten up the substitutions?

Answer 3

I know this is a bit late, but since the accepted answer is still wrong, I thought I'd post my answer for the sake of completeness.

---

The six statements in the questions can be interpreted as follows:

Ignoring case and punctuation, all the words can be substitued in each statement to form mathematical equations.

which gives the following key:

equals = is, minus = without
Y = yes, N = no, T = the
a = a/an, t = to, A = answer

which tranforms the statements into this:

(1) No, an answer is the cube without A, No?

N × a × A = (T³ - a) × N
6 × 4 × 1 = (2³ - 4) × 6

(2) The Yes is No.

T × Y = N
2 × 3 = 6

(3) The squared answer, Yes, is to an answer.

T² × A × Y = t × a × A
2² × 1 × 3 = 3 × 4 × 1

(4) A Yes without the Yes is to the answer.

(a × Y) - (T × Y) = t × T × A
(4 × 3) - (2 × 3) = 3 × 2 × 1

(5) Yes, the answer is No.

Y × T × A = N
3 × 2 × 1 = 6

(6) Yes, the answer to a no is 432.

Y × T × A × t × a × N = 432
3 × 2 × 1 × 3 × 4 × 6 = 432

But how do I know this is the right result?

Mostly trial and error (sorry, no fancy algebra ;-)

From (6), it can been seen that none of the variables is zero, and from (2) and (5) it's also easy to see that A (the answer) must equal one. So the factors of 432 (2⁴ & 3³) must be shared out between the other variables.

I haven't checked all the possibilities, but my solution above definitely works, and it's easy to show that, e.g. Y = 4, T = 3 doesn't:

Y × T × A × t × a × N = 432
4 × 3 × 1 × ? × ? × 12 = 432

so:

t = 3, a = 1 or t = 1, a = 3

but substituting in (4), we get:

(a × Y) - (T × Y) = t × T × A
(1 × 4) - (3 × 4) = 3 × 3 × 1
(3 × 4) - (3 × 4) = 1 × 3 × 1

which is obviously wrong.