# A Logical Puzzle

Here is a block of cipher text C:

28 49 3d 57 2f 48 20 7c 20 7b 4e 7d 3a 49 27 57 27 48 20 45 29 20 3c 2d 2d 20 28 7b 5f 5a 7d 3a 58 20 7c 20 7b 36 5f 27 30 27 38 5f 7d 3a 58 20 41 29

Please evaluate this text and return to me it's value. There aren't many steps to get through but you'll need some knowledge and logic. If you can't get through a particular step, at least post your partial progress so someone else can hep out.

In the interest of improving this puzzle, allow me add a light hint regarding the method of getting the answer: Assuming C is the initial text provided and D is the resulting text after manipulations,

D="ROT180"(A^-1(H^-1(C)))

From there, you will need to use logic to evaluate D and provide the final answer.

• Converting from hex to ASCII, I got (I=W/H | {N}:I'W'H E) <-- ({Z}:X | {6'0'8_}:X A) – AJL Jul 20 '15 at 15:18
• I believe the stackexchange formatting may have modified your text. I did not foresee this being a problem. Are there escape characters for this formatting? – NeedAName Jul 20 '15 at 15:28
• @NeedAName You can use backticks for that like this <don't screw up>. – mmking Jul 20 '15 at 15:39
• @AJL you may want to repost your result with the escape characters mentioned by mmking. – NeedAName Jul 20 '15 at 15:59
• Ah, wait, the text Z}:X | {6 was enclosed in underscores, making it italics. It's actually (I=W/H | {N}:I'W'H E) <-- ({_Z}:X | {6_'0'8_}:X A). AHHH IT WORKED! Sorry... – AJL Jul 20 '15 at 17:28

I interpret this answer to be

True

Because

The statement appears to say $\forall_{x\in\{-8,0,-9\}}x\in\mathbb{Z}^{-}\implies\exists_{H,M,I\in\mathbb{N}}H/M=I$; that is, "(for all $X$ in the set $\{-8,0,-9\}$, $X$ is in the set of negative integers) implies (there exists an $H$, $M$, and $I$ in the natural (counting) numbers such that $H/M = I$). The second statement has no $X$ so we can reduce the statement to: there exists an $H$, $M$, and $I$ in the natural numbers such that $H/M=I$. $6$, $3$, and $2$ are all natural numbers and $6/3=2$; thus the statement is true.

I'm not sure I've interpreted all the symbols correctly, but I feel confident it's at least a partial answer.

• Sorry about the delay in accepting; you interpreted all of the symbols correctly and got the correct answer! – NeedAName Jul 22 '15 at 14:29

Partial answer, following the hint given:

D="ROT180"(A^-1(H^-1(C))) is very clear in its meaning:

"un-Hex" the ciphertext, "un-Ascii" it, then rotate it 180°.

As already stated in the comments, the first two actions give:

(I=W/H | {N}:I'W'H E) <-- ({_Z}:X | {6_'0'8_}:X A)

And the last action results in this:

Now, I can definitely recognize something here, but the notation is throwing me off quite a bit. I'll try to figure out the missing pieces.

• The confusion may be coming from the symbol '|'. In my formal logic courses, this symbol was used like a 'such that', used to separate the conditions of variables involved and the claim being made about them. I'm not sure how common the use of that symbol is, however. – NeedAName Jul 21 '15 at 15:46
• Actually I got that, I'm more concerned about the : and the generic meaning of the line. – Aioros Jul 21 '15 at 15:48
• The colon I understand to be a viable stand-in for the symbol epsilon (which could not be included in my encoding for the obvious reason) – NeedAName Jul 21 '15 at 16:00
• Ok, I thought so and it makes sense. Now I only have to figure out the rest – Aioros Jul 21 '15 at 16:03
• if it doesn't divulge too big a hint, how do we interpret "{ }". Since colon is epsilon which I did not know before. – beginner 101 Jul 22 '15 at 1:42