ThePortForum.com

Observations.

If {[octagon] = 0};
then either
{[square] = 1} and {[circle] = 2}
or vice versa.

Then we could interpret the shapes as going from inner, to middle, to outer layer, in that order.

Using ternary notation, we could suppose that

could be either 16 (in ternary, 121) or 23 (ternary 212).

However, the following shapes are a problem:



Obviously this is because they have no middle layer, proceeding directly from inner to outer. Since we have a notation for 0 already, the omission of a layer is problematic. And since we have other figures where the middle layer contains an octagon, we cannot suppose (even were we to want to) that the omission of a layer represents a 0.

We surmised at first that the 'odd two' would either be even or odd, and that the 18 would accordingly be odd or even. But the three outliers have presented us with a new hurdle.

Getting colder.

!

Someone else must take my magic sword and shield, I'm defeated. I have to lie down by this enchanted brook.. Maybe then I'll get some inspiration..

... this is a very long interlude...

OK, call off the dogs, I've got it.

JDAW has downloaded Yellofier (http://www.yellofier.com/) and is remixing his favourite Orb track using port tongs, decanter, decanting funnel etc to reproduce a homage to 'a huge ever growing pulsating brain that rules from the centre of the ulltraworld' (http://www.youtube.com/watch?v=qexS5hBB1C0).

My question I think...

Daniel has come closest. Should I reveal, and call it DJ’s question?

I think we are going to be here a long time otherwise. I'm stuck on concentric layers and orders of magnitude. Phil and Glenn are being detained somewhere so there's no help from them at the moment. Give me a few hours and if no brainwave strikes then we shall call it quits.

Question.

If you were to continue the series (all instances of ≦4 shapes) how many of the shapes I singled out (those with no middle layer) would there be?

Is this sign ≦ incorrectly, or at least ungrammatically named? Should it be called 'fewer than or equal to'?

djewesbury wrote:Question.

If you were to continue the series (all instances of ≦4 shapes) how many of the shapes I singled out (those with no middle layer) would there be?

Some. Irrelevant.

djewesbury wrote:Is this sign ≦ incorrectly, or at least ungrammatically named? Should it be called 'fewer than or equal to'?

Careful. ‟≦” ≠ ‟≤”.

jdaw1 wrote:

djewesbury wrote:Is this sign ≦ incorrectly, or at least ungrammatically named? Should it be called 'fewer than or equal to'?

Careful. ‟≦” ≠ ‟≤”.

Sorry. My eyesight. I rephrase. Is this sign, ≤, incorrectly, or at least ungrammatically named? [...]

Regarding the quiz, I fear I am now snowblind and cannot see past my previous incorrect deductions. Please, put us out of our misery.

The answer, of course, is that the two squares are odd.

Maybe further explanation is needed. The pictures represent integers in base 4. Obviously no shape is a 0, the shape of smallest area (circle) is a 1, next-smallest (octagon) is a 2, and the largest (square) is the 3. There are three digit positions, innermost (smallest) being least significant, and outermost (largest) being most significant.

Hence:


= 0×4² + 0×4 + 2, a prime


= 1×4² + 3×4 + 1 = 29, a prime


= 0×4² + 1×4 + 1 = 5, a prime


= 3×4² + 1×4 + 1 = 53, a prime

row break


= 1×4² + 0×4 + 1 = 17, a prime


= 2×4² + 1×4 + 1 = 37, a prime


= 1×4² + 3×4 + 3 = 31, a prime


= 3×4² + 2×4 + 3 = 59, a prime

row break


= 1×4² + 2×4 + 1 = 25, an odd square


= 3×4² + 3×4 + 1 = 61, a prime


= 1×4² + 0×4 + 3 = 19, a prime


= 2×4² + 2×4 + 1 = 41, a prime

row break


= 3×4² + 0×4 + 1 = 49, an odd square


= 2×4² + 2×4 + 3 = 43, a prime


= 0×4² + 1×4 + 3 = 7, a prime


= 1×4² + 1×4 + 3 = 23, a prime

row break


= 2×4² + 3×4 + 3 = 47, a prime


= 0×4² + 0×4 + 3 = 3, a prime


= 0×4² + 2×4 + 3 = 11, a prime


= 0×4² + 3×4 + 1 = 13, a prime


So there are the eighteen primes that are ≥2 and ≤64, and also two odd squares, 25 and 49, which are therefore the oddities.


Easy peasy lemon squeezy.

And for those wishing to generate variants on this puzzle, the PostScript code follows:

Daniel’s question.

I'm a little breathless at the complexity of that (admittedly fiendishly excellent) quiz. I thought these were meant to be useless?? How are we supposed to follow that??

I might need some time. Don't be surprised, though, if I come back with a quiz that revolves around your detailed knowledge of Althusserian aesthetics. Or philosophers who have killed themselves.

I was preoccupied for the weekend, but had thought that the answer was probably base 4 in some way. I even had the order of digits (none, circle, octagon, square) figured out correctly. Because, really, Julian wouldn't have done it any other way. I doubt I would have gotten to primes, though, as I was still stuck on encoding and trying to figure out how to make them represent letters.

Fair warning: I have zero artistic talent. I fear Daniel's next question.

jdaw1 wrote:There is an easy observation that provides a key.

Out of interest, what was the easy observation that would have provided the key?

djewesbury wrote:I thought these were meant to be useless?? How are we supposed to follow that??

This is a much easier question that JDAW's mind-numbingly obscure question that should have been asked on a more appropriate forum where replies have a modest chance of being posted by people who have not sat down with a glass / decanter / magnum of port for a relaxing time.

Point of order though Mr Jewsbury. The rules only allow one question, although you can ask a single question in two parts. I shall presume you have asked your question in two parts. My answers are therefore:

• They are meant to be useless
• With a very simple question just like the one you have posed

Am I correct? Is it my turn? I have a very easy question that is to do with Port...

Go Alex, nick the ball while no ones looking...

I too like Glen was just about to solve that absurdly easy quiz.

Oh and;

AHB wrote:Am I correct? Is it my turn?

Yes and yes; my go... (just kidding)

RAYC wrote:Out of interest, what was the easy observation that would have provided the key?

Innermost shape always present and only once an octagon. Which I thought would lead a numerate mind to the only even prime.

It was stupid of me not to advance my thinking one order and decide that 0=nothing. And once one had got that, the notion of them all being primes but for the two squares would have followed. And Glenn is of course right, the order of shapes is something that we spoke of earlier and should have been divined from knowledge of the workings of Julian's very orderly mind. But I think there were perhaps too many layers in this puzzle. And I start to think that my SMWS bottling numbers quiz was very straightforward in comparison.

Where's Derek?

djewesbury wrote:Or philosophers who have killed themselves.

Happily, ∃ en.wikipedia.org/wiki/Category:Philosophers_who_committed_suicide.

jdaw1 wrote:

djewesbury wrote:Or philosophers who have killed themselves.

Happily, ∃ en.wikipedia.org/wiki/Category:Philosophers_who_committed_suicide.

And who liked prime numbers.

AHB wrote:

djewesbury wrote:I thought these were meant to be useless?? How are we supposed to follow that??

This is a much easier question that JDAW's mind-numbingly obscure question that should have been asked on a more appropriate forum where replies have a modest chance of being posted by people who have not sat down with a glass / decanter / magnum of port for a relaxing time.

Point of order though Mr Jewsbury. The rules only allow one question, although you can ask a single question in two parts. I shall presume you have asked your question in two parts. My answers are therefore:

• They are meant to be useless
• With a very simple question just like the one you have posed

Am I correct? Is it my turn? I have a very easy question that is to do with Port...

May I say that this is the post that has made me laugh most in the last little while. Closely followed by Owen's reply.

DRT wrote:

LGTrotter wrote:Where does all this Warre LBV hide until its maturity?

Narnia.

Owen, despite what you've said about BFW, you might be interested in this auction... http://www.bidforwine.co.uk/auctions/show/52088

Oh Daniel, you are lovely! Thanks.

The plot thickens... It should really be PW's question next...

PhilW, in an email, wrote:I'm away in Derbyshire at the moment, so email access only (no forum, dammit, since i'd worked out the primes, too!)

C'mon, don't be a tease. You have now been offered this twice now and shilly shallied (wasn't there a king who had to do this?), or give it to Alex, he said he had a question.

LGTrotter wrote:C'mon, don't be a tease. You have now been offered this twice now and shilly shallied (wasn't there a king who had to do this?), or give it to Alex, he said he had a question.

Actually, I will think of a question. But not tonight. I have to finish my lecture.... zzzzz

That was a whole day ago. And?

And then, today, I gave the lecture, and some seminars also. And became stern with a non-attendee.

The question:

What is the connection between the oboe and Uranus?

Both are mentioned on en.wikipedia.org/wiki/William_Herschel?

Excellent! Your turn!

The Wiseman household has partaken of two alcoholic refreshments this evening. The second was a Rioja. What was the first no more precision being required for the first than was given for the second?

Champagne!

Whisky

Both of the proffered answers are of the correct type, but alas have the wrong value.

Chardonnay.

djewesbury wrote:Chardonnay.

No.

I have another guess. Unfortunate that it's not my go.

Port!

Glenn E. wrote:Port!

An excellent guess, but this time wrong. (Though Port would have been more likely after rather than before Rioja.)

jdaw1 wrote:

Glenn E. wrote:Port!

An excellent guess, but this time wrong. (Though Port would have been more likely after rather than before Rioja.)

This clause makes no sense to me at all. Who are you and what have you done with Julian?

Not complicated: Rioja-then-Port more likely than Port-then-Rioja. And the question said that the missing drink was had before the Rioja.

beer
you were thirsty when you got home from work
so a beer against the thirst and a Rioja for pleasure

AW77 wrote:beer

No.

New Zealand Sauvignon Blanc.

djewesbury wrote:New Zealand Sauvignon Blanc.

‟White wine” would have been sufficiently specific, but would also have been wrong.

The correct answer is something I am known to like.

Cider? (or as we call it in the US, hard cider?)