` This is getting ridiculous. Not only do I have to covertly access the internet (accounting for the lack of fun little posts), but I have yet to post on this blog through MAL, my all-powerful supercomputer. He's not working terribly well at the moment because most of his parts have apparently been infested with blueberry monsters.

` In fact, I have recently been attacked by a blueberry monster. No, I am not talking about the nutritious juice drink called 'Blueberry B Monster' - here I mean a ferocious creature that ripped up my hand and stained a good pair of pants!

` ...That's what happens when the lid to the specimen jar breaks.

*And it was the last one in its liquid phase!!*

` But this is not the time to cry over spilled blueberry monsters. In fact, I have many more important things to cry over. Such as MAL being out of order and my having to resort to the black market in order to acquire the appropriate strange and unusual spare parts.

` My mind is actually spinning like it used to when I was a little freak-girl and I would be forced to solve all these horrendously tricky puzzles in order to lower my self-esteem. If only I'd had MAL around to tell me how perversely twisted these things really were.

` (Heck - if only I had him now in order to continue my work! But, I digress....)

` The most insidious puzzle of them all was the seemingly-simple axiom of the SEQ system. I liked working it, but the emotions it elicited did nothing but ruin my self-confidence.

` Why don't you try it yourself at your own emotional risk? Since you're under no pressure, it should be fun!

` Your starting point is SE. Your ending point is SQ. There are four rules which determine how one can manipulate your letters - It's fairly straightforward:

` First off, you can add a Q onto the end of a string in which the last letter is E. By this rule, SEE can become SEEQ!

` Secondly, one can double a string of letters after S. For example, SEEQ can become SEEQEEQ.

` The third rule states that if you have three Es in a row, you can turn them into one Q. The string SEEQEEE can become SEEQQ.

` Lastly, two Qs in a row can be subtracted from any part of a string. Therefore; SQEQQ can become SQE.

` So, let's say you start out with SE... you can do one of two things - Add a Q or duplicate.

` If you add Q, you get SEQ.

` After that, you could replcate like so: SEQEQ => SEQEQEQEQ.

` If you instead duplicated the initial E, you would have SEE!

` And then, you could add a Q and wind up with SEEQ. After that, the only available step afterward would be to duplicate it to SEEQEEEQ.

` Or, if you wound up with SEEEE, you could duplicate it and get SEEEEEEEE or add a Q for SEEEEQ, or turn any of three Es (in a row) into Qs, thereby getting SEQ or SQE.

` It goes on and on... try working out the rules for yourself!

` Eventually, I was expected to get to SQ. In fact, I even tried working the problem backwards, and that was when I realized the whole trick.

` Now, if you are seriously going at this puzzle, I am sure you can tell me exactly why it was meant to break me!

## 11 comments:

Well, you see, it's very simple:

SQQEEEE QEQEQ QEQEQEQ SQEEQEQEQEQQEQEE QEEEQE QEEQ EQEQQE QEQ E QE QEQEQEQEQEQQE EEEEEQEQEQEQEQEQEQE!

Wow! I was actually just working on SQEEE! I have figured out why it was used to torture you, but I don't want to ruin it for everyone else...

Yeah,

that'sit!` Well-done!

Thank you! ...Since nobody else has bothered to work on it - apparently!- shall I tell you what I found?

` Grah... well, let's give it one more day.

As far as I can tell, you need to duplicate Es ad nauseum such that they collapse into Qs with no Es left over. A Q can be added to the end before the collapse starts, so either an even or odd number of EEE groups is acceptable. Thus the following equation must be solved with integers if the original problem is to be solvable:

2^n = x*3

2^n will never have a factor of 3, so there is no solution to the SQE system.

Incidentally, is your user ID based on this problem?

` Indeed it is. And you are absolutely correct, D. Matter: The problem would be easily solvable if it started with something like

SEEE! All you'd need to do is this:` Double:

SEEEEEE` Add Q:

SEEEEEEQ` Covert all the E's to Qs:

SQQQ` Subtract two:

SQ` Alas...

SQEEE, you, as a multiple of three, are not a theorem of this system....or, y'know, just turn SEEE directly into SQ. But yeah.

Maybe she's trying to confound us all with superfluous logic as part of a mind-control experiment?

` Drat! They've caught onto my evil plan!

` ...DM is the only one standing in my way, with... what is that, the

fourthtime he's corrected me?` Onto my next scheme!

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