Find the Queen..revisited.

This question first appeared on this blog a couple of years back.

Check out my 10th July 2005 post:

"Five Clues - One for each 10 of 50"

The question was this...

You have three cards, (two aces and a queen), all face down. You are asked to find the queen, and you are asked to pick one card only. Then, the magician looks at them all, and promptly turns face up an ace. What is the probability that your card is the queen?

The answer is a third, since you made the choice when all three were face down.

NOW consider the same scenario...

You have three cards, (two aces and a queen), all face down. You are asked to find the queen, and you are asked to pick one card only. Then, the magician looks at them all, and promptly turns face up, an ace.

Your delicate finger is still on the card you chose before any were revealed, and YOU KNOW the probability is 1/3 that yours is the queen.

So, you have 3 cards, two face down, and an ace face up. You have tiny finger on your face down card, knowing that it is 1/3 that it is the one queen.

Now, lift you finger up, really carefully. You have 3 cards, one face up, an ace, and two face down, the other ace and the queen. You are then asked to make your choice again, so you put your same finger down, ever more carefully, ON THE SAME CARD YOU CHOSE BEFORE.

NOW, what is the probability that your card is the queen?

The astonishing answer is that it is now 1/2.

So....what changed between your lifting your finger off the card, to replacing it back, to cause this change in probability?

Moreover, is the answer different if you had chosen the other card instead?

Comments welcome.

The Numbers Quiz - Solutions

1 -- 26 Letters of the Alphabet

2 -- 7 Days of the week

3 -- 7 Wonders of the World

4 -- 12 Signs of the Zodiac

5 -- 66 Books of the Bible

6 -- 52 Cards in a Pack (Without Jokers)

7 -- 13 Stripes in the United States Flag

8 -- 18 Holes on a Golf Course

9 -- 39 Books of the Old Testament

10 -- 5 Toes on a Foot

11 -- 90 Degrees in a Right Angle

12 -- 3 Blind Mice (See How They Run)

13 -- 32 is the Temperature in Degrees Fahrenheit at which Water Freezes

14 -- 15 Players in a Rugby Team

15 -- 3 Wheels on a Tricycle

16 -- 100 Cents in a Dollar

17 -- 11 Players in a Football (Soccer) Team

18 -- 12 Months in a Year

19 -- 13 is Unlucky for Some

20 -- 8 Tentacles on a Octopus

21 -- 29 Days in February in a Leap Year

22 -- 27 Books in the New Testament

23 -- 365 Days in a Year

24 -- 13 Loaves in a Bakers Dozen

25 -- 52 Weeks in a Year

26 -- 9 Lives of a Cat

27 -- 60 Minutes in a Hour

28 -- 4 Base Sequences in Genetics

29 -- 64 Squares on a Chess Board

30 -- 6 Balls to an Over in Cricket

32 -- 100 Years in a Century

33 -- 15 Men on a Dead Mans Chest

34 -- 1001 Arabian Nights

35 -- Death of a 1000 Cuts

36 -- 7107 Islands of the Philippines

37 -- 8 Legs on a Snooker Table

38 -- 3 Legs on a Milking Stool

39 -- 40 Days and Nights of the Great Flood

40 -- 4 Books in a Tetrology

41 -- 2.54 Centimeters in an Iinch

42 -- 99 Red Balloons by Nena

43 -- 4 Dimensions in General Relativity

44 -- 20 Beds on a Dart Board

45 -- 5 Main Terrestial Television channels In UK

46 -- 44 International Dialling Code for UK

47 -- 747 Jumbo Jet

48 -- The 3 Stooges

49 -- 3.1415926 = Pi to 7 Decimal Places

50 -- 20 Teams in the English Premier League

The Time Travel Paradox

A lot of people think that time travel to the past is just a matter of time.

An example of the problems therein is illustrated by the following paradox:

1. You build a time machine.

2. You travel back in time.

3. You meet your own grandfather when he is 20 years old.

4. He is so shocked he dies of a heart attack when you tell him who you are.

5. He never meets your grandmother, they never marry and never beget your mother.

6. You are never born.

7. So because you don't exist, you never build the time machine.

8. Without the time machine, your grandfather cannot die, therefore you are born.

9. So you build the time machine.

10 (See step 2)

Many scientists think that time travel into the past is impossible because of this reasoning.

Movie makers have made use of this idea in subtle ways. Star Trek IV; The Voyage Home uses transparent aluminum. Scottie gives the scientist of 1984 the formula for transparent aluminum, which is of course an invention from the future.

They then use it in the movie, giving credit that it was invented in 1984. So the invention originated in 1984. The question is: Where did the knowledge come from?

Another better example was in the Terminator movies. In T1, the Terminator was sent back through time to kill the hero's mother, because the machines were losing the battle in the future, the hero leading the humans seemingly to victory.

In T3, the third Terminator is again sent back to kill the hero, and to get to him, infects the machines with a virus. The virus causes the 3rd world war, and subsequently the new war against the machines, which the machines start to lose, triggering an action to send a machine (T1) back into the past to kill the Hero before he becomes powerful enough to lead the humans seemingly to victory.....

The loop is quite clear, although James Cameron wraps it up within 3 movies and a gamut of special effects.

This post is closely related to http://phdnotdph.blogspot.com/2005/07/is-time-travel-possible-honest-answer.html
But the point of view is diametrically opposed.


As Douglas Addams once said, the main problem with time travel is not the above, but of "tense". How on earth can you describe something which would have been done if you had done something else in the past future of the future past?

If you look carefully at the two examples, you will see the proof.

Can You Get Them All (in an hour)?

This Quizz's origins come from a magazine called OMNI. However, I have added 20 of my own.

Find the missing words. Method: Read the sentence and use the clues.

Example:

0 -- 24 H in a D is "24 Hours in a Day"

Good luck! (Hint: Copy and paste and print the whole page)

1 -- 26 L of the A ____________________________________________


2 -- 7 D of the W ____________________________________________


3 -- 7 W of the W ____________________________________________


4 -- 12 S of the Z ____________________________________________


5 -- 66 B of the B ____________________________________________


6 -- 52 C in a P (WJs) _________________________________________


7 -- 13 S in the USF __________________________________________


8 -- 18 H on a G C ___________________________________________


9 -- 39 B of the O T __________________________________________


10 -- 5 T on a F _____________________________________________


11 -- 90 D in a R A ___________________________________________


12 -- 3 B M (S H T R) _________________________________________


13 -- 32 is the T in D F at which W F

_________________________________________________________


14 -- 15 P in a R T ____________________________________________


15 -- 3 W on a T _____________________________________________


16 -- 100 C in a D ____________________________________________


17 -- 11 P in a F (S) T _________________________________________


18 -- 12 M in a Y ____________________________________________


19 -- 13=UFS _______________________________________________


20 -- 8 T on a O _____________________________________________


21 -- 29 D in F in a L Y ________________________________________


22 -- 27 B in the N T __________________________________________


23 -- 365 D in a Y ____________________________________________


24 -- 13 L in a B D ____________________________________________


25 -- 52 W in a Y _____________________________________________


26 -- 9 L of a C _______________________________________________


27 -- 60 M in a H _____________________________________________


28 -- 23 P of C in the HB _______________________________________


29 -- 64 S on a C B ____________________________________________


30 -- 6 B to an O in C __________________________________________


31 -- 1000 Y in a M ___________________________________________


32 -- 15 M on a D M C _________________________________________


33 -- 147 M S in a Frame of S ___________________________________


34 -- 1001 A N ______________________________________________


35 -- D of a 1000 C ___________________________________________


36 -- 7107 I of the P __________________________________________


37 -- 8 L on a S T ____________________________________________


38 -- 3 L on a M S ___________________________________________


39 -- 40 D and N of the G F ____________________________________


40 -- 4 B in a T _____________________________________________


41 -- 2.54 c in an I ___________________________________________


42 -- 99 R B by N ____________________________________________


43 -- 4 D in G R _____________________________________________


44 -- 20 B on a D B ___________________________________________


45 -- 5 M T T V c In UK ______________________________________


46 -- 44 I D C for UK ________________________________________


47 -- 747 J J _______________________________________________


48 -- T 3 S ________________________________________________


49 -- 3.1415926 = P to 7 D P ___________________________________


50 -- 20 T in the E P L _______________________________________

How many did you get?

First batch:

Alpha) If an airplane gets 'lift' from its wings, how can it fly upside down?

In the case where there are no airlons, and attachments to adjust the "angle of attack", and airplane with just wing-shaped wings is impossible to fly upside down, as "lift" would trurn into"drop".

Bethe) If I toss a coin onto the nearest table, why is the probability that it will be heads NOT 1/2?

The probability that a coin toss onto a table (NOT the hand) is NOT 1/2 because of the possibility, however unlikely, that it will land on edge and stay there.

Gamow) What is the probability that YOU have more then the average number of limbs?

The probability that YOU have more than the average number of limbs is so close to unity, it makes no difference. Recalling that the "average number of limbs" is simply the total number of limbs divided by the number of people counted, the answer is almost certainly 3.99999999 and not 4, as some people will NOT have 4 limbs. Also, there will almost certainly be more people with less than 4 , than people with more than 4, so this makes the "average" just less than 4.

Second Batch:

1. What is the only word in the English language to have two consecutive "I"s?

Skiing.

2. What is the only word in the English language to have 4 (whoops - 3) sets of consecutive double letters?

Bookkeeper

3. What is the longest word in English with no vowels?

Rhythms

4. What is the only word in the English language that changes pronunciation when captialtised?

"to polish" means to make something shine or to clean; "to be Polish" means being from the country of Poland.

5. True or false: " This sentence is false."

The sentence is neither true nor false. This is a veritable can of worms. I have already written a post about the implications ", viz: ( This sentence is false......? )

6. True or false: "Thes sentence has foure mistokes in it. "

True. There are four mistakes, the fourth being that the number you can see is three, whilst it says "four".

7. True or false : "This sentence is six words long if it were six words shorter. "

True. Take the last six words away, it becomes another sentence of six words.

8. True or false: "This plong contains many non-braspish English doodocks but the overall klerpendall can be spackried from the context."

True. translation" This sentence contains many non-standard English words, but the overall meaning can be inferred from the context"

Apologies for number 2. I put this forward as proof that I do not "search" for any of these.

So you think you know Japanese?

1. What is the only word in the English language to have two consecutive "I"s?

2. What is the only word in the English language to have 4 sets of consecutive double letters?

3. What is the longest word in English with no vowels?

4. What is the only word in the English language that changes pronunciation when captialtised?

5. True or false: " This sentence is false."

6. True or false: "Thes sentence has foure mistokes in it. "

7. True or false : "This sentence is six words long if it were six words shorter. "

8. True or false: "This plong contains many non-braspish English doodocks but the overall klerpendall can be spackried from the context."


Have fun!

A bit of Fun.....

Here are a few (more lighthearted ones), then....

Alpha) If an airplane gets 'lift' from its wings, how can it fly upside down?

Bethe) If I toss a coin onto the nearest table, why is the probability that it will be heads NOT 1/2?

Gamow) What is the probability that YOU have more then the average number of limbs?

Five out of Six ain't bad....

1)You have two coins in your pocket that add up to 26 cents. One of them is not a quarter. What are the coins? (easy)

Solution: A quarter and a penny. The one that is NOT the quarter is the penny. A play on words.

2) A cylindrical hole 6 inches long is drilled straight through the center of a solid sphere. What is the volume remaining in the sphere? (hard)

Solution: 36 Pi cubic inches.

If you want to avoid the calculations in Solution 1, simply take a look directly at Solution 2 below it.

Solution 1
Let R be the radius of the sphere. As the illustration indicates, the radius of the cylindrical hole will then be the square root of R² - 9, and the altitude of the spherical caps at each end of the cylinder will be R - 3. To determine the residue after the cylinder and caps have been removed, we add the volume of the cylinder, 6π(R² - 9), to twice the volume of the spherical cap, and subtract the total from the volume of the sphere, 4πR³/3. The volume of the cap is obtained by the following formula, in which A stands for its altitude and r for its radius: πA(3r² + A²)/6.

When this computation is made, all terms obligingly cancel out except 36π - the volume of the residue in cubic inches. In other words, the residue is constant regardless of the hole's diameter or the size of the sphere!

Solution 2
John W. Campbell, Jr., editor of Astounding Science Fiction, was one of several readers who solved the sphere problem quickly by reasoning adroitly as follows: The problem would not be given unless it has a unique solution. If it has a unique solution, the volume must be a constant which would hold even when the hole is reduced to zero radius. Therefore the residue must equal the volume of a sphere with a diameter of six inches, namely 36π.

3) Three rabbits are crossing the road, a busy road. A father rabbit, a mother rabbit, and a baby rabbit. Suddenly the strong father rabbit sees a chance, takes up baby in his arm, and drags the mother rabbit by the other hand across the road. They arrive there without injury. The baby rabbit then says "Thank you daddy, for getting all two of us across the road safely" Please explain. (medium)

Solution: The baby rabbit was so young it could not count beyond two.

4) You have three cards, (two aces and a queen), all face down. You are asked to find the queen, and you are asked to pick one card only. Then , the magician looks at them all, and promptly turns face up , an ace. What is the probability that your card is the queen? (hard)

Solution: 1 in 3. The probability that your card is the Queen is 1 in 3 because you chose it before the magician turned over any cards. In fact, at any time after the choice, he can always turn over an ace. Try it with the whole pack – it is easier to see then. The dealer then turns over 50 cards that are NOT your chosen one. In this case, the probability remains 1 in 52, As the magician can ALWAYS turn face up 50 cards that are NOT yours!!! Poor Jeffrey!

5) A snail falls into a well which is 20 meters deep. He starts to climb up immediately, and in the daytime, he goes three meters up, but at night falls two meters back again. Assuming he starts the ascent at dawn on the first day, how many days is it before he emerges? (easy)

Solution: 18 days. After 17 days and nights, he is 3 meters below the rim. On the morning of the 18th day, he simply climbs up his lasy daily 3 meters to EMERGE triumphant.

Five Clues........One for each 10 of the 50 comments.

At most, you have between you, three of these original five correct. here are some clues to help you along.....


1) You have two coins in your pocket that add up to 26 cents. One of them is not a quarter. What are the coins? (easy)
Clue: It's a play on words.

2) A cylindrical hole 6 inches long is drilled straight through the center of a solid sphere. What is the volume remaining in the sphere? (hard)
Clue: This can be solved in 3 ways, from hardest to easiest........calculus, algebra, logic.

3) Three rabbits are crossing the road, a busy road. A father rabbit, a mother rabbit, and a baby rabbit. Suddenly the strong father rabbit sees a chance, takes up baby in his arm, and drags the mother rabbit by the other hand across the road. They arrive there without injury. The baby rabbit then says "Thank you daddy, for getting all two of us across the road safely" Please explain. (medium)
Clue: You need lateral thinking.

4) You have three cards, (two aces and a queen), all face down. You are asked to find the queen, and you are asked to pick one card only. Then , the magician looks at them all, and promptly turns face up , an ace. What is the probability that your card is the queen? (hard)
Clue: the answer is counter-intuitive.

5) A snail falls into a well which is 20 meters deep. He starts to climb up immediately, and in the daytime, he goes three meters up, but at night falls two meters back again. Assuming he starts the ascent at dawn on the first day, how many days is it before he emerges? (easy)
Clue: This is math plus a little bit of logic.

Try again, guys, and I MAY continues with the left-right conundrum (if not, then you get a sharp rap on the (left-right) knuckles) .

Solutions Often Bring New Problems.....

.......as we scientists know. It often happens, solve one problem, and a whole plethora of new ones rear their ugly collective head in protest.

I am about to prove that this not only happens in Physics, it happens in blogs as well.

Recall that strange picture I posted on August 15th, entitled

Not a Math Riddle for a Change......

If not, have a look at it. Only five comments, though.

Here is the same image followed by two subsequent others:




The first image is the original puzzle. The second a fraction of a second later, and the third, later still.



When I say 'later' I mean about '1/10,000,000' th of a second.

It is of course, a nuclear bomb, photographed very soon after detonation.

Not in Nevada, but New Mexico. In fact, it is Trinity. The curious shapes seen are a feature of the vaporisation of the tower it was on, visible in photo 1. It was so hot, the sand was turned to glass, and the Indians sell the pieces for $1 each. I have one myself!

Well, that is the solution.

For that, there is a price, as promised. More new problems, as here the students have just started returning to the University.

How many can you answer? Just five for perusal, and for you all to comment upon.

1) You have two coins in your pocket that add up to 26 cents. One of them is not a quarter. What are the coins? (easy)

2) A cylindrical hole 6 inches long is drilled straight through the center of a solid sphere. What is the volume remaining in the sphere? (hard)

3) Three rabbits are crossing the road, a busy road. A father rabbit, a mother rabbit, and a baby rabbit. Suddenly the strong father rabbit sees a chance, takes up baby in his arm, and drags the mother rabbit by the other hand across the road. They arrive there without injury. The baby rabbit then says "Thank you daddy, for getting all two of us across the road safely" Please explain. (medium)

4) You have three cards, (two aces and a queen), all face down. You are asked to find the queen, and you are asked to pick one card only. Then , the magician looks at them all, and promptly turns face up , an ace. What is the probability that your card is the queen? (hard)

5) A snail falls into a well which is 20 meters deep. He starts to climb up immediately, and in the daytime, he goes three meters up, but at night falls two meters back again. Assuming he starts the ascent at dawn on the first day, how many days is it before he emerges? (easy)

Blame it on the freshers, who never do any work in the first week anyway.

Isn't this lovely?

As of 26 September, no-one here has even got three out of five correct yet, and you all must be punished by a sixth, since no-one has remembered my birthday (Hey - look it up, I know you are smart-ish).

This one is insuperably difficult, and if anyone gets THIS correct, and I am satisfied that the answer is original, AND you understand it, then the reward shall be a gift from you to me and I will forget that you forgot.

6) What is the difference between left and right?

So certain am I? So certain I am.

Not a Math Riddle for a Change......

Is it a lollipop? is it a balloon? Is it cotton Candy?

NO it's......

...well........ what do you think it is?

Clues, it is not a sea anaenome, nor is it anything fluffy. In fact, you would very DEFINITELY not want to cuddle this....

It is not bubble gum.....

It ain't a cloud, nor is it a UFO, not even a weather balloon....

This unretouched photo was taken from 7 miles away.

The tower you see is about 33 meters tall.

Got it yet?

Put you answers in the comments, if you please!

Any opinions will be hotly debated, I promise!

As of September 10th, only 5 comments! Come on Guys, you have to be more eager than that!

Marry Charisma's!

2006 is upon us and this blog is seriously out of date. The latest post is dated October 15, and is below the 3-jet post. I still have to figure out why.

Meanwhile, checkout my latest brain-teaser.....

"How many people do you have to invite to a party to be able to say there's more than a 50-50 chance of any two having the same birthday?"

Whilst thoughts abound on that, I will be trying to think of more thunks to think a thunking thing about, that "wioll haven be" a new and pointed post about physics.

10 bonus points for those who can suss where "and how" "wioll haven be" came from.

20 bonus points for identifying where "and how" came from!

How times have changed!