Spinning Dancer

There are three kinds of the people. Some people watching the spinning dancer see her spinning clockwise. Other people see her spinning counterclockwise. The other ones see her changing the direction of the spin. In fact if you try to experiment for a while you could learn your brain to “tell” her to change the direction.

Some people believe that the direction of the perceived spin correlates with the lateralization of the brain (clockwise: intuitive right hemisphere – counterclockwise: analytical left hemisphere). If you want you can believe in that as well.

Maybe it's Coriolis' fault.

We’re in the thread “puzzles & jokes” so I can’t be sure whether you puzzle us or you joke on us. Of course it isn’t that.

The illusion is rather well explained on that page: “In reality, the spinning dancer illusion is related to bistable perception in which an ambiguous 2-dimensional figure can be seen in from two different perspectives”.

Three further links add more detailed information: 1, 2, and 3.

I had the problem to comprehend why some poster decided to share with us in the thread focused on the puzzles and the jokes his beliefs and the citations from The Holy Bible in posts #9 and #28. These confessions and quotations are enigmatic and fun indeed but it seemed to me that they simply don’t match the sophisticated level of the mysteriousness and humor which are peculiar to our thread. I was wrong.

Finally I managed to comprehend everything thanks to the deepen analysis of 2 Peter 3:9. The quotation from the post #28 taken from 2 Peter 3:3–7 was a valuable hint. Thank you, myglide.

Here’s 2 Peter 3:9 (KJV):

(The emphasis is mine.)

That citation is obviously about Pat (Patrick, the Lord) and Slack (Slackware, slack). We’re wards of our Lord (Pat). He’s long-suffering for us. He’s not willing to perish anyone of us. He’s willing to come all of us to the repentance. (My Lord, forgive me because I run Linux Mint sometimes but to excuse me I’d like to confess that I do that in order to convert some infidel people to Linux before I start to convert them to Slackware.) The slackness is the period between the consecutive Slackware releases. Let’s be patient men – the plaything of God (Pat).

As I see now when one has the proper attitude the interpretation of The Holy Bible is a piece of cake. It’s very fun as well.

While this thread seems to be back on track I should make clear. A constructive, positive atmosphere, sharing knowledge and open discussions are among the things that make LQ great. To keep things that way the LQ Rules state you will always behave with respect for others and without personal attacks because those will not be tolerated. Should anyone feel they're not capable of addressing an issue the way we would like to see it then there are two choices: either report a post or thread or keep yourself from posting.
There are no exceptions to this rule and all members are treated equal.

If the above isn't clear then you are invited to email me or any other LQ moderator.

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Raymond Smullyan among the other things is an American mathematician and logician. He’s also the author of the books including mathematical and logical puzzles. One of them is entitled: “The Lady or the Tiger? and Other Logic Puzzles”. In that book there are 12 puzzles concerning “the lady/tiger problem”...

Some king keeps in a prison 12 prisoners (I added to them one prisoner more). Some day he decides to try them one by one. He commands to prepare two rooms. In each room can be the lady or the tiger. The consecutive prisoners should choose just one room. When a prisoner will choose the room with the lady he’ll wed her and he’s free but when he’ll choose the room with the tiger he’ll die killed by the animal.

(In my opinion “the lady/tiger problem” is slightly more complicated because some people probably prefer to be eaten by the tiger than to be married by the lady – on the other hand when one will wed the lady he isn’t necessary free as a result. So we should assume for a while that the lady’s room is the good one and the tiger’s room is the bad one.)

There are three possibilities. Either in some room is the lady and in the other room is the tiger, or in both rooms are the ladies, or in both rooms are the tigers. In the first case it matters which room the prisoner will choose. In the second and the third cases it doesn’t matter though in the second case the prisoner has the good luck and in the third case he has the bad luck.

To make the choice possible on each door is a plate including some information – true or false. The prisoners’ task is to guess which room is the good one (if any).

From among first eight puzzles about the lady and the tiger I chose two puzzles thought up by R. Smullyan and I added to them one puzzle which I thought up.

I skipped first six problems because in my opinion they’re too easy. That doesn’t mean that the following three puzzles are hard. They’re easy as well but not too easy.

***

After a few prisoners solved the puzzles the king decided to complicate the problem. The additional rule says:

If in the room #1 is the lady the inscription on the plate on the door is true but if in the room #1 is the tiger that inscription is false. And – conversely – if in the room #2 is the lady the inscription on the door is false but if in the room #2 is the tiger the inscription is true.

Puzzle 6A

(That’s the puzzle which I invented inspired by the puzzle 6.)

The prisoner #6A sees the following plates:

Which room should he choose?

Puzzle 7

The servants changed the plates on the doors and the occupants of the rooms.

The prisoner #7 sees the following plates:

Which room should he choose?

***

In the next puzzle the inscriptions are ready but the plates aren’t fixed to the doors. The king said to the prisoner that he can solve the problem watching just these two unfixed plates.

Puzzle 8

The prisoner #8 sees two unfixed plates:

Which room should he choose?

If the lady is in 1, expr = True. Thus, the lady must be in both. If the lady is in 2, expr = False. Thus, it does matter which room, which must be false. Therefore the lady is not in 1.

If the tiger is in 2, expr = True. Thus, the tiger must be in both. If the tiger is in 1, expr = False. Thus, it does matter which room, which must be false. Therefore the tiger is not in 2.

If the lady is in 2, expr = False. Thus, the tiger must be in 1. If the tiger is in 1, expr = False. Thus, it does matter which room, which is true since the lady is in 2. Therefore, the tiger is in 1, and the lady is in 2 (choose 2).
If the lady is in 2, expr = False. Thus, you will not win choosing the first room, which means the tiger must be in 1. If the tiger is in 1, expr = False. Thus, it does not matter which room you choose, which must be false. Therefore, the lady is not in 2.

If the tiger is in 1, expr = False. Thus, it does not matter which room you choose, meaning the tiger must also be in 2. If the tiger is in 2, expr = True. Thus, you will win choosing the first room, which must be false. Thus, the tiger is not in 1.

If the lady is in 1, expr = True. Thus, it does matter which room you choose, so the tiger must be in 2. If the tiger is in 2, expr = True. Thus, you will win choosing the first room, which is true if the lady is in 1.

Therefore, the lady is in 1, the tiger in 2 (choose 1).
I have to make an assumption here which may be incorrect. By "There's the tiger in that room" I assume you mean the room behind that same door -- "that room" could also mean the *other* room so I'm not positive which you meant. I will assume it means the same room with the sign attached.

Assume #1 = "Tiger in this room" and #2 = "Tigers in both rooms".
If the lady is in 1, expr = True. But obviously the lady is not a tiger. Thus, the lady cannot be in 1.

If the tiger is in 2, expr = True. Thus, the tiger must be in both rooms. If the tiger is in 1, expr = False. Thus, 'tiger in this room' is false, which is wrong. Thus, the tiger cannot be in 2.

If the lady is in 2, expr = False. Thus, tigers are not in both rooms, which is fine. We know lady cannot be in 1. If the tiger is in 1, expr = False. Thus, 'tiger in this room' is false, which is wrong.

Thus, the labels must not be correct.

Assume #1 = "Tigers in both rooms" and #2 = "Tiger in this room".
If the lady is in 1, expr = True. Obviously 'Tigers in both rooms' cannot be true, so the lady cannot be in 1.

If the tiger is in 2, expr = True. Thus, 'Tiger in this room' is true, which is fine. If tiger is in 1, expr = False. Thus, 'tigers in both rooms' is false, which is wrong. If the lady is in 1, expr = True. Thus, "Tigers in both rooms" is true, which is wrong. Thus, the tiger cannot be in 2, because neither lady nor tiger could be in 1.

If the lady is in 2, expr = False. Thus, 'Tiger in this room' is false, which is fine. If the tiger is in 1, expr = False. Thus, 'Tigers in both rooms' is false, which is fine. Thus, the tiger is in 1, and the lady in 2 (choose 2).

If I misunderstood and the sign should have meant "Tiger in other room" then you would still choose 2, and the assignments would be "#1: Tiger in other room" and "#2: Tigers in both rooms".

(That took me much longer to type than to solve, and I don't feel like proofreading. My explanation also sounds like a scene from The Princess Bride. Inconceivable!)

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lol... Best post in this thread so far!

P.S.
Shouldn't this thread be moved to the non-*nix general forum?

T3slider,

everyone else,

The present thread is entitled “Puzzles & Jokes (Off-Topic Topic)”. So we publish here the puzzles and the jokes. It isn’t necessary to put here the solutions. In my opinion the solutions disturb the fluent reading of the thread and the intimate thinking.

Moreover to solve each above “tiger/lady problem” is enough to think for a dozen of the seconds. To write the solution of each puzzle it takes a dozen of the minutes. It’s the waste of your time. The published solutions cause also that the entire thread swells.

So if you can restrain yourself from publishing the solutions – do that. Don’t publish them here.

Try instead to find a nice puzzle or joke and put it in that thread. Look for something puzzling or joyful. Try to keep close to the average level of the thread or elevate it with something really sophisticated. Don’t lower it significantly with something obviously stupid or plainly offensive.

The exception: if according to your research your solution is unique feel free to publish it here. (For example: the 12 marbles or “fake coin” problem described in the post #4 has more than just one obvious solution and some of them are really impressive. So each new solution of that problem would be very interesting and valuable.)

(I put the excerpt from the above in the first post as “Our Rules”.)

Thank you for correcting me. My English is so-so and I translated these puzzles from Polish to English. Now – according to your suggestion – I changed the description on the first plate from “There’s the tiger in that room” to “There’s the tiger in this room”.

***

You tried to describe the complete solutions. As a result they ignore the economics of the thinking.

Example:

At that point one should assume that the first assumption is false so: #1 = “Tigers in both rooms” and #2 = “Tiger in this room”.

(As a result of their completeness the reading of your solutions is tiresome and most of the people will skip some parts of your solutions – the same as I did.)

I wrote about that in the second paragraph above.

Guys and gals: don’t publish your solutions here if it isn’t necessary indeed!

It seems that the average Slackware Linux user is much smarter than the average computer user. So moving that thread from “Slackware” to “General” section of LinuxQuestions.org forum would lower significantly the level of the thread. It would cause also the unwelcome disturbances with some dumb people publishing here some stupid or offensive content. (I have no mercy for the dumbness and I’m the founder and the maintainer of that thread.)

So I think that it’s good idea for us – Slackware Linux users – to have our own smart fork of the “General” section in that thread kept in the “Slackware” section.

***

I observe carefully the work of our moderators and I see that they’re very smart. They not only react to something what happened in the past but they can also stop something what could happen in the future. Examples: post #63 somewhere else and post #35 here. (In both these examples by the accident it was the same moderator but that doesn’t matter – all our moderators are smart and I’m proud that I can be a part of the community gathering smart users and smart moderators.)

Stupid is as stupid does (sorry, I really cannot resist)

I get the same answer when I type:

Take care: your system is probably infected by Ad14 virus. It causes respiratory infection in the software resulting in the wrong calculations made by the individual programs. By default it adds 14 to the result but in some rare cases paradoxical reaction appears and it subtracts 14 from the result.

rkelsen,

According to my calculations:

It seems that your system isn’t infected by the mentioned virus but it uses 0 as a dividend or as a factor.

The other hypothesis: your machine uses in the calculations the following equation:

As a result:

I’m not sure whether it’s a good or a bad news.