# 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, 2015 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? Jul 20, 2015 at 15:28
• @NeedAName You can use backticks for that like this <don't screw up>. Jul 20, 2015 at 15:39
• @AJL you may want to repost your result with the escape characters mentioned by mmking. Jul 20, 2015 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, 2015 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! Jul 22, 2015 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°.

(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. Jul 21, 2015 at 15:46
• Actually I got that, I'm more concerned about the : and the generic meaning of the line. Jul 21, 2015 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) Jul 21, 2015 at 16:00
• Ok, I thought so and it makes sense. Now I only have to figure out the rest Jul 21, 2015 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. Jul 22, 2015 at 1:42