The Sphinx's Lair - 2017-10-21

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Gareth McCaughan

12:56 AM

@phroureo I've looked at it briefly, considered whether indexing into the websites using the digits of the access times leads anywhere (not obviously), wondered idly whether the victim's name might indicate a Baconian cipher (5 bits per letter, encoded in things like font changes, odd/even, capital/lower, etc.) but not taken the trouble to try e.g. treating the digits of the times that way (maybe after converting 12h->24h), and decided to leave it for others with more energy for now.

3 hours later…

4:14 AM

0

Q: Rock around the old oak tree

I am the reason Ireland doesn't sink, And what sometimes keeps people from the drink, Rotten rotten me, almost proved Fermat, I'm not Fahrenheit, my choice tells you that.

riddle word trivia humor

3 hours later…

7:25 AM

Re C4: DE[ed] + FINANCE ~ DEFIANCE is close but not quite in a few ways hmm

7:59 AM

1

Q: How many lemon?

A king announced to his subjects that "Who ever brings me 2 lemons from the magic garden, will be crowned as king" One clever young man dared to go in search of the lemons. He came near the first door if the garden. The guard told the young man that "When you return you should give me half of th...

@Sp3000 Probably time for a hint. Any preference on what type?

First letter, probably (unless anyone else has other preferences)

CCCC hint: first letter is C

3 hours later…

11:12 AM

1

Q: Arrange six cigarettes in such a way that each cigarette touches every other cigarette

What are some ways to arrange six cigarettes in such a way that each cigarette touches every other cigarette?

geometry combinatorics

11:26 AM

I would have thought this hint to be helpful but I still don't get this wordplay at all

Well, good luck everyone

12:19 PM

One of the hints I have is the eye of Providence.

Does this make sense to anyone? "They trust us we trust them"

American dollar bills contain both the eye of Providence and "In god we trust" on them.

@Apep got that. Apparently, that's not the answer.

Is there any other content to it, or is it just the eye and that phrase?

the document is titled SEC. That's it.

We have to get a password to access the doc and then solve.

12:44 PM

So, the answer is the password to the next one and that's how you confirm?

@Apep yeah?

2 hours later…

3:01 PM

how do you guys get to chat from the main site now? the top bar no longer works

The furthest right icon in the header.

Gareth McCaughan

Just to be more explicit: clicking on that produces a dropdown menu, and one of the things in that menu is chat for the site you're currently on. It's ... not obvious at a glance that that's what it will do, but it does :-).

Oh, i see it, thanks!

yeah, before clicking the stackexchange icon produced that menu

Someone solve this C4. It's hurting my head now...

defiance is the only 8 letter word i can think of

3:11 PM

back could be champion

or title back could be eltit

or just E

Gareth McCaughan

I want it to be CON + [half of title] and mean "back" as in "support", but I can't find anything that does that.

@thecoder16 Rubio's told us that it begins with C.

ah

or back as in reverse

contrary, converse?

Gareth McCaughan

not sure that either of those can really be defined by "back"...

3:30 PM

I was thinking CONFIDES, but I can't think of a title that FIDES is half of.

P.S. I am lost when it comes to cryptic crosswords

I think it would have to be "backs" in that case.

Well, I know FIDE is a title.

and it can be half of title if you are creative enough. But, 7!=8.

@Apep Don't take this as either confirmation or refutation of anything being said here, but why would it have to be "backs"?

plural?

Gareth McCaughan

you don't actually mean plural

3:34 PM

@Rubio The verb tense would be different otherwise... unless there's another part of speech in which they would be equivalent.

Of course not, I meant tense...

(slaps head in disgust)

Oh. I ... nevermind, I mis-parsed your thought entirely :)

Gareth McCaughan

(Although CON for opposition seems kinda plausible to me, I'm not 100% convinced by it and I hope my earlier comment hasn't got everyone looking for CON- words.)

@Sid "Inflected", rather than plural, really.

@GarethMcCaughan No, I only mentioned my thought because I had it yesterday, before you said anything

3:37 PM

@Rubio That was just me semi-drained with this hunt I am in...

So, forgive me speaking hopeless things sometimes...

@Sid I see, FIDE is a chess title.

Gareth McCaughan

@Apep I wondered about CHAMPION too; seems like that would need CON (around the outside) to be "opposition" but I can't see how to make HAMPI be "half of title". (It's a bit less than half of CHAMPIONSHIP but that would be horrible for all sorts of reasons.)

president -> CONSIDE(R)? Though I assume "half" isn't going to refer to the "middle half" of anything?

"half" to take the middle half of something doesn't sound like something I'd do. :)

4:01 PM

For a moment there I was confused because I didn't notice Rubio changed avvies

I'm briefly messing with y'all. :)

@Rubio And that confirms our theory. :P

Why, I have no idea what you might mean.

3 hours later…

7:15 PM

0

Q: What connects these names?

What relation do these five names share. Henry Eddie Murray Vic Roy

connections-puzzle

7:28 PM

0

Q: Dice problem involving nine randomly selected cups

I was given this problem by a colleague, and I cannot figure it out. Given nine cups and an unlimited supply of six-sided dice rolled one at a time, what is the probability that you will, at some point, obtain a value of exactly seven in each of the nine cups, if the cup into which any given dic...

probability dice

7:51 PM

I'm answering that

it's taking a while

8:10 PM

Clue 31 is on the way! Expected to release in the next couple days, faster the sooner I find a good Sudoko generator that I copy into a text editor and change the numbers...

hint: there is a sudoku in clue 31

oh, man. this problem is degenerating into a mess.

I could tell that just from reading it xD

@ffao it's going to be tagged sudoku so that's not a big hint :P

I'd be surprised if there was a solution that didn't get messy

8:12 PM

me too, but i didn't realize how bad it would be. the answer for just 1 cup is already $\alpha = \frac{70993}{279936}$

it's also equivalent to hitting (7,7,7,7,7,7,7,7,7) in a suitably defined random walk in $\mathbb{Z}^9$

I guess I quit, I don't have time for this :| I mean, I do, but I don't care enough to keep typing. And I'm 90% certain the asker won't understand the answer anyway.

also, I edited docs.google.com/document/d/… to include a short explanation

if I were to try solving this I guess I wouldn't attack it without a computer

true, there are not many paths inside that box with U(1,6) steps

x

that's a smarter solution

nevermind, you have to try all paths out to 63 steps in 9 dimensions

@Mithrandir cc @Beastly since you mentioned it at some point recently

forget I said anything, I'm a moron

2

8:16 PM

@EricTressler it's amazing how often people say stuff like that in Puzzling.SE hosted rooms

oh wow, 30 was in May

this isn't even a puzzle, it belongs on math

in that case VTC

I'm trying to make sure the answer isn't alpha^9 before I close this window, though

but I think probability is on topic

no, it is not alpha^9. I stop

@Mithrandir it is, certainly, but puzzles should have nice solutions

8:18 PM

well, you don't have to actually simulate it

I was thinking of splitting all 7s into dice rolls first, then reordering those to get the probability

but that would get more complex than just simulating

@Mithrandir glad you've gone back to finish them off :)

well, it's easy to get that, since it's just all the partitions of 7 except {7}

So if you say represent the partitions of 7 by a polynomial in which the coefficient of x^n is the number of ways to make 7 with n dice, then you can raise it to the power of 9 in the end

and then divide each nonzero term by 6^n and sum to get the probability

I think. This is really making me wish I had spent more time with generating functions

8:34 PM

It's still going to get really ugly without a computer

@ffao Have you seen Peter Winkler's book of puzzles? amazon.com/Mathematical-Puzzles-Connoisseurs-Peter-Winkler/dp/…

Gareth McCaughan

@EricTressler @ffao That book is one of two; the other is called "Mathematical Mind-Benders" and is also good.

It led me to spend a lot of time trying to prove the union-closed set conjecture

Gareth McCaughan

Ha!

and also to spend a lot of time looking at purported proofs of that conjecture for their mistakes

@GarethMcCaughan it is somewhat related to the research I was doing at the time, so it was only a partial waste of time

I might buy a copy of his other book

@GarethMcCaughan I assume you've also read Martin Gardner, then?

Gareth McCaughan

8:51 PM

@EricTressler I'm not sure whether you have a particular bit of Gardner in mind, but yes, I think I've read most of it.

I think I've read all of his work, so I don't have anything specific in mind

Gareth McCaughan

9:21 PM

here's a Gardneresque thing I just heard about: Take a unit cube. Place it in space however you like. Project it onto the (x,y)-plane and the z-axis. Look at the measures of its shadows -- that is, the area of the set of (x,y) for (x,y,z) in the cube, and the length of the interval of z for (x,y,z) in the cube. Theorem: These are equal. Generalization: do it in any number of dimensions, and partition the dimensions into two however you like. So e.g. if you take a unit 4-cube anywhere in R^4, ...

... the measures of {(w,x) : (w,x,y,z) in the cube} and {(y,z) : (w,x,y,z) in the cube} are equal.

The proof in 1 or 2 dimensions is trivial. The proof in 3 dimensions is (I think -- I haven't tried to prove it myself) rather easy. The proof in higher dimensions is (I am told) quite tricky.

(The relevant paper is by Peter McMullen, it's in the Bulletin of the London Mathematical Society, and it's only 3 pages long. So I guess it can't be that tricky.)

(Well, a very short paper can be very tricky indeed. But chances are it's not too bad.)

that's surprising

I believe it for a unit cube in 2 dimensions. I'll have to think about why it's true in 3 dimensions

unit square?

@Wen1now unit 1-cube

Round of codenames?

can't right now, but I will play in about 6 hours if anyone's around then

Gareth McCaughan

9:32 PM

unit square = unit 2-cube. unit interval = unit 1-cube. ordinary unit cube = unit 3-cube.

@GarethMcCaughan is the unit cube the unique shape with that property?

@Wen1now sure, although it's 12:35AM and I won't SM

@GarethMcCaughan I guess, of the simplices + sphere that extend naturally to n dimensions. Nevermind, there aren't enough objects to consider to make that an interesting angle

The paper actually answers my question

Volumes of Projections of Unit Cubes is followed 3 years later with Volumes of Complementary Projections of Convex Polytopes

@GarethMcCaughan I thought a unit square = unit 1-cube because the 'surface' is 1-dimensional, in the same way a 2-sphere is the 3-dimensional sphere

@boboquack that kind of terminological confusion mostly comes up with the sphere

@boboquack the unit $n$-cube lives in $n$ dimensions, but the $n$-sphere lives in $n+1$ dimensions

9:43 PM

OK, another case of me thinking I understand something that I don't :P

it's really just specialized terminology for the sphere, because the surface of the sphere is important. nobody cares about the surface of the cube

I think maybe I'm not helping

puzzling.stackexchange.com/search?q=surface+of+a+cube+is%3Aq

12 questions :P

@boboquack you got me, I love hyperbole :-p

Gareth McCaughan

@EricTressler Yes, the followup paper establishes which other polytopes have the same sort of property.

9:57 PM

@EricTressler I'm not able to learn from books for some reason, so I don't read a lot

Hmm. I'm not getting any TSL (1) things in the title bar for some reason

10:16 PM

World Puzzling Championship 2017 ended today, Ken Endo won

@Wen1now do you get the donk?

Not sure. My sound is very low

Try another message...

I've turned the sound up

@Wen1now donk

Yeah got the sound

10:43 PM

There is nothing for me to review :(

@micsthepick surely there are 20 gazillion SO posts up for review?

Not in the categories that are available for the 500-1000 rep user in just puzzling :(

10:59 PM

Hi everyone

Hi.?

11:36 PM

Something popped up on the late answer queue, and I said no action needed, does that qualify me for a new badge?

Huh?

If you've never reviewed anything in that queue before, yes, you'll get a bronze badge.

I only recently earned the privilege of accessing review queues

But are you sure that no action was needed?

puzzling.stackexchange.com/help/badges/82/custodian

You just got the badge

E.g a comment left explaining proper answer format (spoilers), an edit, a vote (up or down)...

11:39 PM

Interestingly, Wen only just reviewed their first late answer too

It looked like a valid answer (but the question was not shown)

@micsthepick yes it was - grayed out below

I think.

The question is typically below the answer you're reviewing, faded, iirc.

okay, I will keep that in mind the next time I review.

11:53 PM

@Mithrandir did you do anything for that review?

reviewing is fun

@micsthepick what review?

the late answer from today

What do you mean?

There were at least 2 today.

11:57 PM

Once you review it, it's out of the queue.

The latest one (puzzling.stackexchange.com/review/late-answers/stats only shows one from today)

puzzling.stackexchange.com/users/41731/eedrah has been doing quite a few late answers

^ eedrah has been solving some pretty tough ones - very cool :)

Oh, do you mean the answer that I reviewed?

I left a comment:

-2

A: Unexpected hanging paradox

I think that

And edited.

And downvoted.

Who can review reviews?

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