Math Is Fun Forum

  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#26 Re: Puzzles and Games » The Professor and the Student » 2012-03-23 18:52:41

The only logic, of all I've seen, that I accept is that of bobbym.

So I give him 5 votes. That's not what is usually thought of as democracy, which I abhor. I'm all for meritocracy, though.



I believe that Friday remains in contention, but not because of this logic.

#27 Re: Puzzles and Games » The Professor and the Student » 2012-03-22 19:56:00

Interesting, but by my reckoning I make the score about 5 - 5, and I myself am voting for both sides. (so far)

#28 Re: Puzzles and Games » The Professor and the Student » 2012-03-22 12:28:49

Wednesday dead and buried already - I didn't think we were going to get so far so soon ...

But seriously, I think bobbym is onto something here. Random picking is logically out, because it amounts to Russian roulette, the prof will have to rely on his luck to vindicate himself. God help him if the random picker chooses Friday or Thursday, because he's going to look very, very stupid... so I am inclined to think also that this is not a logic problem really, more a philosophical, semantic problem to do with the meaning of words like "know".

Imagine trying to set up a machine that could perform all the parts of the professor's role. And make his claims about "who" would "know" what. I don't see how such a machine could be constructed.

So my answer to the riddle is that nothing can be known, ever. The world might end tomorrow, so the professor has no right to say the test will happen at all. And equally the students will never "know" anything anyway. But I'm not really satisfied with that either.

#29 Re: Puzzles and Games » The Professor and the Student » 2012-03-22 12:06:02

bobbym wrote:

Maybe not. If the professor chose Wednesday on the Friday before, when Tuesday came around the students could deduce the test is tomorrow,since Thursday and Friday are out.

Oops, Wednesday is starting to look decidedly dicey...

... the slower we go, the further we'll get, as the tortoise said to the hare.

#30 Re: Puzzles and Games » The Professor and the Student » 2012-03-22 12:02:05

anonim, I saw you were in a hurry to get onto Wednesday, and now you are going back to Thursday! You're making me nervous! I was going to post

slowly, slowly catchee monkey... "They stumble that run fast" (Romeo and Juliet, if I remember correctly)

but then I saw bobbym's carefully considered post and I thought that would make things clearer ... but apparently not.

And while I was typing this I saw there was another post in the meantime but if I have to abort every time I'll never get a word in...

#31 Re: Puzzles and Games » The Professor and the Student » 2012-03-22 11:21:00

It seems that the later the test, the more impossible it becomes. So MIF seems to be playing it fairly safe by plumping for Wednesday. But is it safe enough? But first let's get the full picture on Friday... because I have a feeling that if Friday goes down the drain, there'll be no stopping the collapse...

#32 Re: Puzzles and Games » The Professor and the Student » 2012-03-22 06:31:10

Hi Phrontister,

Notice, in Bob's post, the following:"
Because, for example, at the end of Wednesday the logic is "We've reached the end of Wednesday, so it could be on Thursday or Friday".
"
But you say you think it can't be on Friday, whereas Bob is suggesting that it can be. This difference needs to be settled. If we are to reach agreement.

#33 Re: Puzzles and Games » The Professor and the Student » 2012-03-21 18:11:18

wintersolstice wrote:
bob bundy wrote:

hi

Of course, I agree with amberzak!  smile

But for reasons of logic too.

The deduction "We've reached the end of Thursday, so it must be on Friday" is sound.

but this does not allow you to deduce anything about earlier days.

Because, for example, at the end of Wednesday the logic is "We've reached the end of Wednesday, so it could be on Thursday or Friday".  It is always dangerous to keep applying the same logic as the student has done.  And MathsIsFun's answer shows why!

Bob

I don't actually agree with this logic because if they reached the end of Wednesday then it must be Thursday because if it was on Friday it wouldn't be a suprise (because if it hasn't happen by the end of Thursday is has to be Friday)

but that's just my opinion:D I have seen another way (apart from my own) of resolving th paradox so I suppose it show there's more than one way to do it:D

I don't agree with this logic either, and I think your objection (your "because") is valid. I have yet to see one way of resolving this paradox.

I would appreciate it if all those who have an opinion about this problem, would state clearly: Do they think the test could be on Friday, yes or no? That I think would be the best point to start tackling this problem thoroughly.

#34 Re: Puzzles and Games » Code » 2012-03-20 17:11:08

Hi anonim,

I'm following your excursions into the past again... because I've always had an everlasting fascination for codes, spent many, many hours devising bridge bidding systems in the old days when there were not so many restrictions...

I want to add to my puzzles, coded clues! So that the code can be very easily and quickly deciphered. Hiding one 4-letter word in a 12x12 matrix is not my idea of elegance. The following code hides one word in a sequence of 14 letters. To solve:

You can just write the answer down straight away, without having burdened your memory with more than about 5 bits of knowledge.

ASYIFKMKTUBZRB

Warning: The word you are looking for is not valid in scrabble, it's a name and a very rare one at that. It does, however, appear in Google, it's a name of great antiquity.

#35 Re: Puzzles and Games » The Fork! » 2012-03-20 16:33:03

Hi anonim,

After 7 years you dug this up! I see again you are a very thorough person...

I'm glad, because it started with a nice puzzle, which gave three solvers the chance to shine with ever-increasing degrees of brightness... Vulcan taking gold for the simplest and best answer, and the mob resorting to an avalanche of unmaths to bury the shame of their inferiority.

Thanks! You hauling the staff over the coals reminds me of my own behaviour in a past time...

#36 Puzzles and Games » The Professor and the Student » 2012-03-19 17:21:01

gurthbruins
Replies: 91

Here's an old classic: I don't know if it's been aired lately.

The professor said to his class: “I'll be giving you a test one day next week, but you won't know in advance which day.”

“But that's impossible!” objected one student. “If we haven't had the test by end of Thursday's class, then we'll know in advance it must be on Friday. So we can't possibly have the test on Friday, or we'd know in advance.

“That leaves only Monday, Tuesday, Wednesday and Thursday as possible days.
“But if we haven't had the test by end of Wednesday's class, we'll know in advance it must be on Thursday, since we have already ruled Friday out. So we can't have the test on Thursday either, or we'd know in advance.

“That leaves only Monday, Tuesday and Wednesday as possible days.
“But if we haven't had the test by end of Tuesday's class, we'll know in advance it must be on Wednesday, since we have already ruled Friday and Thursday out. So we can't have the test on Wednesday either, or we'd know in advance.

“That leaves only Monday and Tuesday as possible days.
“But if we haven't had the test by end of Monday's class, we'll know in advance it must be on Tuesday, since we have already ruled Friday and Thursday and Wednesday out. So we can't have the test on Tuesday either, or we'd know in advance.

“That leaves only Monday as  a possible day.  So we'll know in advance that the test will be on Monday. So we can't have the test on Monday either, or we'd know in advance.
“So we can't have the test at all.”

Who is right, the professor or the student? I have never seen a satisfactory resolution of this paradoxical argument.

#37 Re: Puzzles and Games » Word Game 23c » 2012-03-19 16:48:22

Hi anonim,

Assuming you mean "whole" post (the "while" puzzled me!) ... there is one correct word in your post: "me."

Seems you like to submit words... but I suppose we must draw the line somewhere - shall we say, from now on, a maximum of ten words per player per day?

But you have vindicated your method by finding a word!

So the list is now

AR
AS
ON
THE
KING
ME

#38 Re: Puzzles and Games » Word Game 23c » 2012-03-19 03:24:03

Hi anonim and hs, welcome to this game!

No correct words yet.

If and when it seems as if you guys have run out of ideas to test, I'll add more words as clues.

#39 Re: Puzzles and Games » Variation of "the hardest logic puzzle" » 2012-03-17 19:50:34

I took a look at the link you posted - looks very interesting - before I look at your variation I'd better start with the original version!
So I'm going to start thinking about that right away. I don't know how long that will take me - we'll see, I'm certainly not going to spoil my fun by looking at what others have done to solve it... until I admit some sort of defeat that is.

#40 Puzzles and Games » Word Game 23c » 2012-03-17 19:38:01

gurthbruins
Replies: 26

Here's a list of five words:

AR
ON
AS
THE
KING

What do these words have in common?
If you think you may have figured it out, please submit a WORD which you think may belong to this group, to test your idea.
If it's on the right track, I'll let you know.

Please don't disclose what your idea is, as that may spoil the game for others.

This game is similar to #66, only much harder I think. For the reason that there are few correct words, so submitting words at random, with no hunch or reason, is not likely to be of help. So I don't want to waste your time by encouraging you to resort to random trial and error.

Have fun!

#41 Re: Puzzles and Games » Word Game #66 » 2012-03-17 19:21:49

wintersolstice wrote:

if this is still on:D

Hi wintersolstice!

Glad to see some renewed interest in my puzzles.

After two years I am finding that this puzzle has been well covered and come to a desirable end. I suggest we go on to new puzzles.
If any of the solvers of this one wish to help you on with it, they are welcome to take it over, however.

I am creating new puzzles now, appearing on my site as mentioned above, and I will put them on other sites as well, the same puzzles and different ones. Anything to increase interest.

See "Word Game 23c" on this thread, coming up in the next hour.

#42 Re: Puzzles and Games » Word Game #66 » 2012-03-16 07:00:37

gurthbruins wrote:

POSITION AT END OF ROUND 9

Valid words: (a ail ale alms art early ears end hew hi hone ill inch lank link lover luck lucky older otter raising reposition rice rover utters)

POINTS:
ZHero.......................... 4 (end)
mathsyperson........... 20 (ail ale alms art hone ill link lover otter)
JaneFairfax................. 1
phrontister................ 21 (a early hew hi inch luck older raising reposition utters)

Phrontister joins mathsyperson, making two players now in the know!

- Those were fun days; I've now become more active with these games once more.


My challenging word games have been solved about six or seven times.

Two solvers emerged from a writer's forum, one from a chess forum, and recently, two from a UKDebate forum.

It would be nice if all these aces could see my newest puzzles, and maybe be not so lonely as they've always been up to now.

I'm inviting you, and will invite them all, to go to my new forum dedicated specially to such puzzles:  http://afroditi.proboards.com .

There  I'll keep some puzzles going. There are no chores of registration - guests can post and start threads - , but of course you would be most welcome to register.

Hope to see you there!
Gurth.

#43 Re: Euler Avenue » Gurth's Fractals » 2012-01-29 19:10:27

The image (post #1 above) is a bit lonesome I think - after a long time, I developed another 3D fractal formula yesterday - it drew nothing but a black space - at midnight I thought the bug might be in a very obvious place, and yes it was - so I had the whole thing fixed up by about 2 am. Here's the pic - I call it "Bananas" (being a fruitarian!)

Bananas21u.jpg

PS: I've now translated my drawing program to VB2008EE language. Copies of the program available on request.

#44 Re: Euler Avenue » Gurth's Egg Cup Theorem » 2011-09-13 18:11:46

namealreadychosen wrote:

What if the egg is exactly turned upside down so that every point which was touching the egg before is not touching it any more? It is necessary to include the upper boundary of the egg cup as part of the egg cup for Gurth's theorem to always hold.

This is basically a case of the theorem that every mapping leaves at least one point unchanged.

- Agreed.

#45 Re: Dark Discussions at Cafe Infinity » Where do you stand? » 2011-01-07 19:48:42

Where I stand on teaching maths:
As a teacher, I expect to be inspired by my pupil. If 'e can't inspire me to teach h', then 'e is not for me and I am not for h'.

#46 Re: Dark Discussions at Cafe Infinity » Flat Earth Society » 2011-01-07 19:23:43

A flat earth (well, ignoring a few mountains and other anomalies) makes some sense. Those living on the bottom side of the disc would think they were on top, just as the New Zealanders probably think they are on top instead of "down under."

And that solves the mystery of exactly where hell is! We of course are all in heaven. Or have I got things upside down?

#49 Euler Avenue » Gurth's Egg Cup Theorem » 2011-01-06 20:43:33

gurthbruins
Replies: 2

A perfectly spherical egg is resting in a perfectly hemispherical egg cup of the same radius.
So that every point on the surface of the cup is touching (mated to) a point on the egg.

The egg is now removed and can be rolled around at random or by design.

The egg is now replaced in the cup. Regardless of how this is done, there will be at least one point on the cup that is touching the same point on the egg as originally.

Board footer

Powered by FluxBB