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My puzzle-pal Anna is in Rome. She's travelling with her husband Morgan, and they're both architects well versed in Math. She wanted to tell me why she liked Rome so much, but instead of directly telling me, she sent me this riddle.

Not loan and return,
Not always even and odd.
Don't get it? Maybe next month
You should ask my husband.

Don't get too stressed,
Life is yours to live!
Just don't think too far forward,
Or you'll end up a heinous pie!

What was she trying to tell me?

The answer is one word.

Hint 1:

Anna is quite the perfectionist.

Hint 2 (to further clarify):

De Morgan's law is required to solve the first two lines. (As deducted by @Rand al'Thor and @M Oehm)
De Morgan's Law state that for two events A and B $\lnot (A \land B) \Rightarrow \lnot A \lor \lnot B$
Which translates to not(A and B) => (not A) or (not B)
If $\lnot A = C$ and $\lnot B = D$
The statement $\lnot A \lor \lnot B = C \lor D$ yes?

Hint 3:

Title contains subtle hint.

Hint 4: (based on @Gareth's answer)

If stressed live => evil desserts (heinous pie)
Why didn't I use "Sweets are bad for you" or "Sahara Satan"?

Hint 5:

In order to truly find the answer.
I will repeat what I have said.
Don't think too far forward.
And follow the words of the Jedi Master.

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  • $\begingroup$ Is it the "Vatican City"?? $\endgroup$ – Anurag Jul 11 '17 at 8:47
  • $\begingroup$ I did say the answer is one word... Hehe @Anurag $\endgroup$ – bolt997 Jul 11 '17 at 8:48
  • $\begingroup$ Maybe next month may refer to Augustus, the first Roman Emperor... $\endgroup$ – Christoph Jul 11 '17 at 9:09
  • $\begingroup$ @Christoph oooh... Close... $\endgroup$ – bolt997 Jul 11 '17 at 9:27
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    $\begingroup$ Just to be clear: is it deliberate that you said "architectures" rather than "architects"? Also, is it deliberate that in the last hint you have "the the" rather than, say, "of the"? $\endgroup$ – Gareth McCaughan Jul 13 '17 at 2:14
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Update

A bit of a guess, but I think the answer is:

Symmetry

because

The Roman architecture is based on classical symmetry (among others)
Palindromes are symmetric
Anna is an architect and a perfectionist (symmetry ~ perfection)

Yet another partial answer

I think I got the first two lines:

Not loan and return,
Not always even and odd.

Borrow or rob
Never odd or even
(Using De Morgan's law and because they are palindromes)

Based on @JFox's comment on hint 1 I think

All (maybe not 3 and 4 as they're already used for Morgan's law) lines have a palindrome match - that or the answer is 6 letters as 6 is the best match for a "perfect" number of letters for a single word

So the first 2 lines in the second stanza would be:

Don't get too stressed,
Life is yours to live!

Desserts I stressed ("Stressed desserts" also works)
Live not on evil

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  • $\begingroup$ Nice! Second stanza was revealed some palindromes, but it's not as "perfect" as the one you found here. Read hint 1 again and hopefully it becomes clear :) $\endgroup$ – bolt997 Jul 18 '17 at 0:37
  • $\begingroup$ Oh, this is looking very impressive. $\endgroup$ – Gareth McCaughan Jul 19 '17 at 11:33
  • $\begingroup$ YES! I wanted the phrase "don't think too far forward" to be taken literally, as in forward -> backwards to hint at palindromes (reading in reverse). Same goes for how the Jedi Master Yoda talks. Other than that, perfect! $\endgroup$ – bolt997 Jul 20 '17 at 0:47
  • $\begingroup$ I think the Yoda one (the only hint I couldn't match) was a bit misleading, he doesn't exactly talk in reverse but uses a passive talk, which made me think I should rearrange the words in the lines to get a clue. Such as "Too stressed, don't get" instead of "Don't get too stressed," $\endgroup$ – Styx Jul 20 '17 at 6:23
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Outrageously speculative and partial answer

In view of hint 3, I think

the title is hinting at the word "palindrome" (pal in Rome...)

at which point

the word "stressed" jumps out at me as being the reversal of "desserts"; together with the mention of pie (suggestive of desserts again) and the injunction not to think forward, I think it very likely that either DESSERTS or something closely related is the answer being sought. Hint 1 does make me wonder whether somehow we have the more specific PARFAIT, or something similar, in view. Oh, and maybe a heinous pie is a rotten tart, which is getting rather like TRATTORIA (or TRATTORIE) backwards, but I think this is probably coincidence.

But this is all very vague and impressionistic, and in particular I haven't figured out those first two lines which are clearly important. But perhaps something in the mess above will help someone who's thinking more clearly about this than I am.

[EDITED to add:] Some scattered thoughts on those first two lines, which haven't got me anywhere useful, in case some cleverer person sees what I'm missing. (Or in case they help JFox to figure out what sort of hint to give next.)

Applying de Morgan seems to turn "not loan and return" into "(not loan) or (not return)". Perhaps "not loan" turns into GIVE or GIFT or SELL or KEEP or something; perhaps "or" represents itself; perhaps "not return" means NOT backwards = TON, or once again KEEP, or something. None of these things seem to fit with one another to make words. [EDITED to add:] JFox has made some comments on another answer that suggest that the words we're looking for on the first line might be BORROW and CARRY, as in arithmetic. Perhaps Anna and Morgan are computer architects. There is a thing in computer hardware called a "carry-lookahead adder" which would match well with the bit about not looking too far forward, but I think that's probably coincidence.

And

applying de Morgan seems to turn "not always even and odd" into "(not always even) or (not odd)". The first of those isn't actually equivalent to "never even", M Oehm's ingenious suggestion, but it might be right. "or not odd" might mean the odd-index letters of OR NOT, or ONT; or, again, "or" might represent itself and "not odd" might yield EVEN or NORMAL or any number of other things. Once again, I don't see anything useful to do with these fragments.

A few other remarks. First,

as well as STRESSED yielding DESSERTS, at the end of the next line we have LIVE yielding EVIL, and EVIL DESSERTS might be a "heinous pie". Perhaps there's some famous thing in Rome to which "evil desserts" could be a clue, but right now I'm failing to think of any.

Second,

we haven't yet made any use of the fact that Anna and Morgan are architects. Despite all the dessert-themed stuff above, my guess is that actually we're looking for something more related to Rome's historic buildings, and the desserts are just a step along the way there. (But, see above, I suspect that actually they are not that sort of architect.)

Third,

presumably the words of the Jedi master here are "do or do not, there is no try".

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    $\begingroup$ SO CLOSE, you are most definitely correct! After you answer the first two lines, I think it will become clear what the answer (that is the word Anna wants to convey to me) is. $\endgroup$ – bolt997 Jul 12 '17 at 0:56
  • $\begingroup$ A rot tartmakes Trattora backwards $\endgroup$ – Christoph Jul 12 '17 at 7:43
  • $\begingroup$ But "trattoria" has an I in it, and while "rotten" kinda means heinous "rot" really doesn't. $\endgroup$ – Gareth McCaughan Jul 12 '17 at 9:39
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    $\begingroup$ Yeah, possibly. I think we need to figure out exactly what's going on in the first two lines -- I suspect that deMorganizing in the right way, followed by interpreting them as some sort of wordplay, will make everything clear. (E.g., having got "not return" as a part of the first line, perhaps that turns into TON or something.) $\endgroup$ – Gareth McCaughan Jul 12 '17 at 11:53
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    $\begingroup$ I like the palindrome hint -- after all, the "pal in Rome" (ouch!) is called Anna. I can't find any obvious use for that hint, but I observe that negating "always even" gives the palindrome "never even". $\endgroup$ – M Oehm Jul 12 '17 at 18:22
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Partial answer

Not loan and return,
Not always even and odd.

Loan and return could refer to interest, and what's always even and odd are the integers. So it's not interest or integers, but maybe something else starting with INTE?

Don't get it? Maybe next month
You should ask my husband.

Next month is August, named after the Roman emperor Augustus, and Anna's husband is Morgan. This looks like a reference to Augustus de Morgan, which fits with the fact that they're "well versed in Math[s]".

Don't get too stressed,
Life is yours to live!
Just don't think too far forward,
Or you'll end up a heinous pie!

I don't get much of this, but the last line is surely a reference to $\pi$, so the "too far forward" could mean that we're looking for something like an infinite series which converges to some pi-related value?

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  • $\begingroup$ You got the second one! +1 now what do you do with it... $\endgroup$ – bolt997 Jul 11 '17 at 15:20
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    $\begingroup$ The first two lines look as if de Morgan's law could, at least formally, be appiled to them: not (loan and return) is (nor loan or not return). But I don't see how that could be useful. $\endgroup$ – M Oehm Jul 11 '17 at 15:24
  • $\begingroup$ @JFox Wait, you mean the second line (even/odd) or the second spoilertag (next month/husband)? $\endgroup$ – Rand al'Thor Jul 11 '17 at 15:35
  • $\begingroup$ Second spoilertag @Rand al'Thor, and yes! You're on track @M Oehm $\endgroup$ – bolt997 Jul 11 '17 at 23:52
  • $\begingroup$ I'm not well versed in architecture but I'd guess that the second stanza has to do with something specifically architectural, what with words like "stress" being bandied about. The 'too far forward' part reminds me of cantilevers, but those work just because of weight on one side, not really because of stresses applied to them. $\endgroup$ – MMAdams Jul 12 '17 at 16:43
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Well, I have a hunch and I think it's

Number

That's because:

You have a loan number and a return number

Then

Numbers are not always necessarily odd or even, they may be real numbers and hence fractions

After that 'Ask my Husband' probably hints at:

Asking by giving him a call at his Phone NUMBER

There is also a saying that:

Age is just a number...and so we must not take stress is life.

And yeah,

The number-system is never ending and thinking too far will lead us nowhere. 'Pie' might refer to it's homophone/mathematical counterpart Pi=3.1415926... And that's never ending too !

Finally...

She's in Rome, s we know there's definitely something called Roman Numbers, right ? Maybe that interested her the most.

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  • $\begingroup$ Very nice try! +1, but it is not the correct answer. Do take note of the "wordplay" tag! $\endgroup$ – bolt997 Jul 11 '17 at 9:07
  • $\begingroup$ You know what @JFox, I had thought the answer to be Augustine , ( The Rome connection's obviously there ) initially...owing to next month (August) and heinous pie...could refer to Catholicism...but I couldn't explain other parts.. $\endgroup$ – Swarnabja Bhaumik Jul 11 '17 at 9:34
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UPDATE 2 -

I am thinking this word that Anna sends somehow describes love . Here's why

Not loan and return,
Not always even and odd.

Lets take !Loan first . I am thinking this means the antonym for Loan. The closest one I could find is Borrow Next, !Return's antonym can be Take Similarly , for !always even = moody, excitable ** And , !odd = **Regular , Conventional . When two people have unconditional love for each other , there is no feeling of "borrowing" or "taking" . It is understood that what's mine is yours too.

Usually , the personalities of the people in love are opposite in nature , so they cancel each other and can live harmoniously. For example - if one person is moody or impulsive , the other person is grounded or conventional or even keeled

This is all I have. Maybe this is a step in the right direction. Hope this helps

UPDATE 1 -

After looking through the hints by Jfox , I think Anna is trying to say

Colosseum

Don't get too stressed, Life is yours to live! Just don't think too far forward, Or you'll end up a heinous pie!

According to my theory , the Colosseum looks very similar to a stack of dominos. Also , the Colosseum has been damaged in a way that looks like the dominos have fallen , which further makes me assume that the line ("Don't get too stressed") refers to the Domino effect. Also the lines (Just don't think too far forward, Or you'll end up a heinous pie) talk about the skirmishes fought inside the Colosseum and spectators throng to watch a poor soul who thinks too far ahead or is in over his head( A poor man falling in love with the Emperor's daughter and gets caught) . Since it is a fight to the death , usually the combatant becomes a bloody pulp (heinous pie!)

ORIGINAL ANSWER

Just a stab at the answer . Is she saying

"DOMINOS"

Explanation

Not loan and return, Not always even and odd. Don't get it? Maybe next month You should ask my husband.

Borrowing from @Rand al'Thor's answer , the first four lines describe the mathematician Augustus de Morgan

Don't get too stressed, Life is yours to live! Just don't think too far forward, Or you'll end up a heinous pie!

Augustus deMorgan , formulated the principle of Mathematical Induction which is demonstrated by a line of Dominos . Also , if you push a single domino (Don't get too stressed) leads to the Domino effect (Or you'll end up a heinous pie! ).Pie is an alias for Pizza. Also , Italy is famous for its Pizza's !!

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  • $\begingroup$ I like this answer, except that in the spoiler hints, it's revealed that the name from lines 3 and 4 is used to solve lines 1 and 2 $\endgroup$ – Luke Bickell Jul 12 '17 at 15:41
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    $\begingroup$ Good try +1! Here's something for you to think about. I recall Anna saying she didn't particularly like the colloseum. Her last trip to Italy, I remember her saying she also despised the pisa tower... $\endgroup$ – bolt997 Jul 13 '17 at 7:15
  • $\begingroup$ Love might even be a good answer, but if so, I think it should come in its Italian form, amore, because that somehow fits the de Morganian syntax: AM OR E: $\endgroup$ – M Oehm Jul 13 '17 at 16:01
  • $\begingroup$ I was thinking the word is "RMA" which is a palindrome for "Roma-Amor" which fits in nicely with the "love" theme. The palindrome is an inscription on an ancient roman brooch $\endgroup$ – Bharath Jul 13 '17 at 18:35
  • $\begingroup$ Just adding to my previous comment , the word "RMA" has been decoded as a palindrome above .. I apologise for wording my comment wrong . $\endgroup$ – Bharath Jul 14 '17 at 6:58
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Arche is the answer !

Roman Architecture is known for construction of arches, which are considered to be the most stable, stronger form of construction than any other comparable in such class.

The keystone of an arche satisfies the lines described in the riddle.

Well, that is based on the description of the lines. However, after relooking at the 'tag' - wordplay, it seems something to do with words !

I can get till this point: Anagram of the keywords - Anna, Rome and Morgan form a phrase which links with why she likes Rome !

Like for example - 'More Roman Again' !

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    $\begingroup$ How does it satisfy the lines of the riddle? Please edit to explain your answer better. $\endgroup$ – Rand al'Thor Jul 11 '17 at 13:41
  • $\begingroup$ Also, please consider using spoiler formatting - so even if you have the correct answer, other people still have time to figure it out on their own. $\endgroup$ – puzzledPig Jul 11 '17 at 14:45
  • $\begingroup$ Thanks @puzzledPig for suggesting usage of formatting options ! $\endgroup$ – Mea Culpa Nay Jul 11 '17 at 15:10
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    $\begingroup$ There is no letter I in Anna+Rome+Morgan. $\endgroup$ – Gareth McCaughan Jul 11 '17 at 17:00

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