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).

In statements 3 and 4, is the word "to" supposed to be "too", as in "truthfully"? If so, then I very likely have the solution. Also, is the lowercase on the "no" in statement 6 deliberate? — COTO, Dec 13 '14 at 09:52
@COTO Everythimg in the puzzle should be assumed as correct unless revised. So unless awesomepi changes the puzzle in any way, base your solution on the content, not assumed mistakes. — warspyking, Dec 13 '14 at 12:41
This is a weird and brilliant puzzle! Are the words 'Yes', 'No', and 'answer' actually code for something else? I'm also wondering if some of the words actually represent only numbers of letters... — Rand al'Thor, Dec 13 '14 at 16:42
I've had a Eureka moment but I can't quite get everything to fit exactly... — Rand al'Thor, Dec 13 '14 at 19:12
Is there a way to "verify" the solution or will the EUREKA be so clear, it isn't needed? — BmyGuest, Dec 14 '14 at 16:41
@BmyGuest There's no way to verify the EUREKA moment, but the answer is pretty clear, you shouldn't get something weird such as giraffe or 3.19503 and like I said, if you solve it as a different puzzle, I'll still upvote it because there are a lot of ways to read this really weird puzzle. Let's just say that the EUREKA moment will be pretty big (it will change how you look at the problem immensely). — awesomepi, Dec 14 '14 at 20:43
@awesomepi I suspect I have the Eureka moment, but I'm still stuck on the puzzle it presents. I'm unsure about the precise implementation of the mechanism, so I'm having trouble logicking my way though. Can I ask, is the punctuation and capitalization a functional part of the puzzle, or is it there for purely aesthetic reasons of making the surface content look good? — xnor, Dec 14 '14 at 23:05
I think I have the trick as well, but similar to xnor I'm stuck. Am I right in assuming the last "What is the answer" actually belongs to the puzzle? — BmyGuest, Dec 15 '14 at 08:53
@BmyGuest It is the question that you are trying to answer, nothing else — awesomepi, Dec 15 '14 at 15:06

Rand al'Thor · Accepted Answer · 2014-12-18T19:40:25.847

29

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.

edited Dec 18 '14 at 19:40

answered Dec 16 '14 at 15:31

Rand al'Thor

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I can't say if you're on the right track, but at least you're on the same track as I am/was - just a good step ahead. I didn't have a clue about how to interpret the 432 line, except that it has to be the key as it contains a plain-text number. – BmyGuest Dec 16 '14 at 16:05
SOOO CLOOOSE, but no cigar. +1 fo' you, but no answer – awesomepi Dec 16 '14 at 17:57
I'm there too, but it's still too arbitrary. – djjeck Dec 16 '14 at 19:40
I was also on the same track. Clever idea with commas meanings chains of equalities. I was stuck on operator arity not matching up but that could resolve – xnor Dec 17 '14 at 05:15
Isn't the used inconsistently in your suggestion? – BmyGuest Dec 17 '14 at 08:20
@awesomepi Any hints as to where he went wrong? – warspyking Dec 17 '14 at 22:31
The small words are a large part of the problem. To is a variable. – awesomepi Dec 18 '14 at 00:53
@awesomepi - Am I right about 'is' and 'without'? – Rand al'Thor Dec 18 '14 at 09:31
Yes, you are... – awesomepi Dec 18 '14 at 17:32
@awesomepi - Do 'a' and 'an' represent the same variable? – Rand al'Thor Dec 18 '14 at 17:37
@randal'thor yes – awesomepi Dec 18 '14 at 17:48
@awesomepi - Edited to include final answer! – Rand al'Thor Dec 18 '14 at 17:57
1

spot the mathematician :p – d'alar'cop Dec 18 '14 at 18:18
@randal'thor, this wasn't the exact answer that I was looking for, I will give it to ya, but I would like you to find TA, or the answer – awesomepi Dec 18 '14 at 19:00
@awesomepi - Fair enough, but now I think I've come to a contradiction! I've probably gone wrong somewhere; will check. – Rand al'Thor Dec 18 '14 at 19:15
@d'alar'cop - What about now? :-p – Rand al'Thor Dec 18 '14 at 19:16
1

@randal'thor. Earlier, I had Y=3 N=6 A=1 a=4 t=3 T=2, and parsed the first statement as NaA = (T³-a)N, which all works out, except for the third statement, which I'm convinced has an error in it. I think it should be "squared", not "cubed". – ekhumoro Dec 18 '14 at 19:18
@ekhumoro It sure looks like it, I'm sorry for all the inconvenience it may have caused. I've changed it. – awesomepi Dec 18 '14 at 19:27
@awesomepi - Done! – Rand al'Thor Dec 18 '14 at 19:40
@randal'thor Wow, I just realized there are two solutions... one is Y=4, N=12, A=1, a=9/8, t=8/3, and T=3, and the other one is: Y=3, N=6, A=1, a=4, t=3, and T=2... – awesomepi Dec 19 '14 at 02:40
@awesomepi There must be a typo in your second solution, since $T=ta$, and in fact $TA=3$ in both cases. Nice puzzle btw! – Rand al'Thor Dec 19 '14 at 11:02

h34 · Answer 2 · 2014-12-17T22:09:44.480

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?

score 1 · Answer 3 · answered Dec 19 '14 at 01:52

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.

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

Well, here's the puzzle:

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

A few more things

3 Answers3

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