The worlds first riddle!

Mark:
AVERAGES
66

MEAN
79

JANE
42

shake hands (paw)

Yeah, but (the dog) would shake your hand.



"I should go to church."

An atheist was taking a walk through the woods, admiring all that the "accident of evolution" had created. "What majestic trees! What powerful rivers! What beautiful animals!" he said to himself. As he walked alongside the river, he heard a rustling in the bushes behind him.
As he turned to look, he saw a seven-foot grizzly charge towards him. He ran as fast as he could up the path. He looked over his shoulder & saw that the bear was closing in on him. He tried to run even faster, so scared that tears were coming to his eyes.

He looked over his shoulder again, and the bear was even closer. His heart was pumping frantically as he tried to run even faster, but he tripped and fell on the ground. He rolled over to pick himself up and saw the bear right on top of him raising his paw to kill him. At that instant, he cried out "Oh my God!"

Just then, time stopped. The bear froze; the forest was silent; the river even stopped moving. A bright light shone upon the man, and a voice came out of the sky saying, "You deny my existence all of these years; teach others I don't exist; even credit my creation to a cosmic accident, and now do you expect me to help you out of this predicament?
Am I to count you as a believer?"

The atheist, ever so proud, looked into the light and said, "It would be rather hypocritical to ask to be a Christian after all these years, but could you make the bear a Christian?"

"Very well," said the voice.

As the light went out, the river ran, and the sounds of the forest continued, the bear put his paw down. The bear then brought both paws together, bowed his head and said, "Lord, I thank you for this food, which I am about to receive."

Amen.



There is a row a soldiers that is 1km in length. They walk with a constant speed in a straight line, in one direction.

At the end walks a messenger, he has to bring a message to the captain walking all the way back at the beginning of the row.

The messenger starts walking past the soldiers and immediately turns around when arriving at the captain and walks back to the end of the row. When the messenger is back at end, the group of soldiers traveled a distance of 1000 meters.

The soldiers and captain are walking at the same constant speed. The messenger (walking faster then the soldiers) is also walking a constant speed.

You don't know anything about time or speed.

How many meters did the messenger travel from the end of the row to the beginning and back



There is a tree standing among others, it has four branches and on every branch there are three bird nests and in every nest there are four eggs and on every egg there are seven spots.

What is the name of the tree



A Medieval riddle:

What is it that never was and never will be




Curves A, B, C, and D, are defined in the plane as follows:

A = { (x,y) : x^2 - y^2 = x/(x^2 + y^2) },

B = { (x,y) : 2xy + y/(x^2 + y^2) = 3 },

C = { (x,y) : x^3 - 3xy^2 + 3y = 1 },

D = { (x,y) : 3yx^2 - 3x - y^3 = 0 }.


Is it possible to prove that the intersection of A and B is equal to the intersection of C and D

"What is it that never was and never will be."

Nothing?

MESSENGER
1+sqrt(2) km

I don't know (I would guess yes), but if you solve A (or B) for (x^2 + y^2) and substitute it into B (or A), you get D. I'm not sure how C figures into it.

"What is it that never was and never will be."

Li'l Turtle:

"Nothing?"

If it was up to me I would say, ?'congratulations'. However, as the answer is, "a mouse's nest in a cat's ear." I will have to limit myself to, ?'good try'.


Mark:

MESSENGER
1+sqrt(2) km


Here is the simple answer:

The messenger has to have traveled 2 km. It doesn't matter what speed they walked at. At the beginning of the puzzle, the line is 1 km long. The general is therefore 1km ahead of him. He must therefore travel more than 1 km to reach the general. Since the line moves 1000 m, or 1 km forward, the end is where the beginning was. Even if he walked 1.5 km to the general, he only has to walk .5 km to get back to the end of the line. It goes faster going back, because now they are coming towards him, and not going away.


AND NOW FOR THE MORE CALCULATED ANSWER:

Let's denote the speed of the line of soldiers by W and the speed of messenger by V. Let t1 denote the time it takes the messenger to reach captain and t2 the time it takes him to get back to the end of the line.

The troop has travelled 1000m in time (t1+t2), so:

1000m = W (t1+t2)

t1+t2 = 1000m/W

At the same time both in time t1 and t2 the messenger travels 1000m relative to the column, so:

t1 = 1000m/(V-W)

t2 = 1000m/(V+W)

This gives equation:

1000m/W = 1000m/(V-W) + 1000m/(V+W)

When you divide the numenators by 1000m, the denominators by W, and denote V/W by A you obtain:

1 = 1/(A-1) + 1/(A+1)

A^2 - 1 = 2A

Solving that quadratic formula for A you obtain 1+sqrt(2) and 1-sqrt(2). Since V/W can't be negative it turns out V/W = 1+sqrt(2).

The distance travelled by the messenger is:

V (t1+t2) = V ( 1000m/(V-W) + 1000m/(V+W) ) = 1000m ( 1/(1-1/A) + 1/(1+1/A) )

After you plug in A and simplify:

1000m ( 1+sqrt(2) )

and that is approximately 2414,21 m.




A and B is equal to the intersection of C and D.

Mark:
I would guess yes.

Good guess.

Let z=x+i*y. Then A and B are the real and imaginary parts of
z^2=3i+1/z, and C, D are likewise Re and Im of z^3-3iz=1, and
the two equations are plainly equivalent. Alternatively, having
seen this, we can formulate a solution that avoids explicitly
invoking the complex numbers, starting with C=xA-yB, D=yA+xB.




The sequence of digits
1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 2 1 ...
Is obtained by writing the positive integers in order. If the 10^n th digit in this sequence occurs in the part of the sequence in which the m-digit numbers are placed, define f(n) to be m. For example f(2) = 2 because the 100th digit enters the sequence in the placement of the two-digit integer 55.

Can anyone find, f(1987)


There is an old story of a trader who put into Philadelphia with a boat load of shingles, some which had been damaged in passage. He was asked by a Quaker merchant what the price was for the shingles.

"They are $10 a bundle," he replied, "if you choose the bundles and $5 a bundle if I choose them."

The merchant thought for a minute and said, "... ".

What is the best deal he could make



Here is a riddle, which involves a similar principle:

A man had an apple stand and sold his larger apples at 3 for a dollar and his smaller apples at 5 for a dollar. When he had just 30 apples of each size left to sell, he asked his son to watch the stand while he had lunch.

When he came back from lunch the apples were all gone and the son gave his father $15. The father questioned his son. "You should have received $10 for the large apples and $6 for the 30 small apples, making $16 dollars in all."

The son looked surprised. "I am sure I gave you all the money I received and I counted the change most carefully. It was difficult to manage without you here, and as there were an equal number of each sized apple left, I sold them all at the average price of 4 for $1. Four goes into 60 15 times so I am sure $15 is correct."

Where did the $1 go

APPLES
To the customers. The average of $1/3 and $1/5 is $4/15. However, the boy sold the apples for $4/16.

60 * $4/15 is $16
but 60 * $4/16 is only $15

Yes. It may not be I, but someone can.

I get f(n) = n + 1 - CEILING(LOG(n - FLOOR(LOG(n))))
f(1987) = 1984

I believe that the question is missing a rather important comma. :wink:
(Am I going mad or have we had this very same issue before?)



Let the trader choose which to give you...but buy all of them.

Mark:

APPLES
To the customers. The average of $1/3 and $1/5 is $4/15. However, the boy sold the apples for $4/16.

60 * $4/15 is $16
but 60 * $4/16 is only $15

Yes, we are talking different amounts.

The large apples were being sold at 3 for a dollar--3/$1 = $0.33333333333 each.

The small apples were being sold at 5 for a dollar--5/$1 = $0.20 each.

The son sold the entire lot at 4 for a dollar--4/$1 = $0.25 each.

The real average between 3 for a dollar and 5 for a dollar is 3 3/4 for a dollar, or $0.26666666 each.

On average, the son lost 1.6666666 cents for each apple he sold, which he did 60 times.



Mark: (Continuing to rewrite math history by proving 1987 was indeed 1984 - move over George Orwell)

I get f(n) = n + 1 - CEILING(LOG(n - FLOOR(LOG(n))))
f(1987) = 1984

What, no WALL LOG?

Counting, we see that the numbers from 1 to n digits take
up (10^n*(9n-1)+1)/9 spaces in the above sequence. Hence we need
to find the least n for which 10^n*(9n-1)+1 > 9*10^1987, but it
is easy to see that n = 1984 is the minimum. Therefore,
f(1987) = 1984.


Adrian:
(Name that tree.)

"I believe that the question is missing a rather important comma."


For those unfamiliar with ?'Dingo Lingo' as reproduced above, may I point out that Adrian has the answer. I.e.: "There is a tree, (<<<missing comma) standing among others,"

(Am I going mad, (<<<missing comma). Affirmative that good buddy.
Or, (<<<missing comma) have we had this very same issue before?)

Your memory is too good.


Best deal he could make?

Adrian:
Let the trader choose which to give you...but buy all of them.


Yes, buy the lot, and let him choose. You get everything half price. Remind me not to negotiate with you. I enjoyed your take on the benefits of diesel.





Problemo:

How many primes among the positive integers, written as usual in base
10, are such that their digits are alternating 1's and 0's, beginning
and ending with 1



Problemo:

Evaluate \int_0^a \int_0^b \exp(\max{b^2 x^2, a^2 y^2}) dy dx where a and b are positive



Problemo
Prove that if 11z^10 + 10iz^9 + 10iz - 11 = 0, then |z| = 1. (Here z is a complex number and i^2 = -1.)




Four men are going on holiday with their families. In general, they like their holiday, but they all have one point of complaint.

For instance, John dislikes the food in the country he visits, because he hates vegetables. Udo from Germany went to China. Dave went skiing on winter holiday. Juan spent his summer holiday in another European country, but thought there was too much rain there.

The winter holiday wasn't spent in Norway. The American went on Christmas holiday. The British hated the fact that he didn't understand the language. The man on Easter holiday was often confused, because he couldn't read the signs in the streets. Dave didn't go to Norway.

The American didn't go to France. Juan from Spain didn't go to Italy.

Which nationality went to Norway

PRIMES
uno (101)

EVALUATE
How about if we just decipher the damn thing?

HOLIDAY
The American

Li'l Turtle did not write a very clever riddle code that spelt out the answer which is now deleted.


Mark:
PRIMES
uno (101)


Exactly one, namely 101. 1 is not prime; 101 is prime. The sum
100^n + 100^{n - 1} + ... + 1 is divisible by 101 if n is odd,
10^n + 10^{n - 1} + ... + 1 if n is even. (To see the second part,
think about 101010101 = 102030201 - 1020100 = 10101^2 - 1010^2.)


Mark:
EVALUATE
How about if we just decipher the damn thing?


Split the inner integral according to the max{}. The easy term becomes an integral of t e^{t^2}. The other term becomes an easy term after you switch the order of integration. The answer should have an e^{(ab)^2}.



HOLIDAY

The nationality is "Spanish"



Some you may have seen before, I see they have now been put together to form an IQ test!


1. Which one of the five choices makes the best comparison? LIVED is to DEVIL as 6323 is to:

a) 2336 b) 6232 c) 3236 d) 3326 e) 6332


2. Which one of these five is least like the other four?

a) Horse b) Kangaroo c) Cow d) Deer e) Donkey


3. Which number should come next? 144 121 100 81 64?

a) 17 b) 19 c) 36 d) 49 e) 50


4. HAND is to Glove as HEAD is to:

a) Hair b) Hat c) Neck d) Earring e) Hairpin


5. A fallacious argument is:

a) Valid b) False c) Necessary d) Disturbing

Tryagain wrote:
"Li'l Turtle did not write a very clever riddle code that spelt out the answer which is now deleted. Split the inner integral..."

Alright, looky here, dear-


Mark wrote:

"EVALUATE
How about if we just decipher the damn thing?" ......o.k. I will-


PRIMES = Paulaj removed instant message, except smile.......

uno = you know! :wink:

(101) = lol

8 - ) = <---that looks like a wise man to me, and he alway's gives 101% (lol) effort.

"HOLIDAY
The American" = All I can do is agree with that statement. I have been working very hard lately, I could use a vacation!

(I love playing with you folks, word games that is )

Should I nominate Try for A2K president? I apaulajize for clogging your thread with my silliness, it's just that I want to play, (the other word games don't thrill me like they used to.)

1. C
2. B
3. D
4. B
5. B

[quote
Alright, looky here, dear-


Mark wrote:

"EVALUATE
How about if we just decipher the damn thing?" ......o.k. I will-


PRIMES = Paulaj removed instant message, except smile.......

uno = you know! :wink:

(101) = lol

8 - ) = <---that looks like a wise man to me, and he alway's gives 101% (lol) effort.

"HOLIDAY
The American" = All I can do is agree with that statement. I have been working very hard lately, I could use a vacation!

(I love playing with you folks, word games that is )

Should I nominate Try for A2K president? I apaulajize for clogging your thread with my silliness, it's just that I want to play, (the other word games don't thrill me like they used to.) [/quote]



That is one of the best posts I have ever read. Amusing and witty in equal measure.

"apaulajize"

A true classic.

Sadly, I must decline the Presidency because I cannot afford a pay cut and the house is not big enough. Silly is what I do best, welcome to the club.



1. C
2. B
3. D
4. B
5. B




7. NASA received three messages in a strange language from a distant planet. The scientists studied the messages and found that "Necor Buldon Slock" means "Danger Rocket Explosion" and "Edwan Mynor Necor"
means "Danger Spaceship Fire" and "Buldon Gimilzor Gondor" means "Bad Gas Explosion".

What does "Slock" mean

a) Danger b) Explosion c) Nothing d) Rocket e) Gas


8. Ann is taller than Jill, and Kelly is shorter than Ann. Which of the following statements would be most accurate

a) Kelly is taller than Jill b) Kelly is shorter than Jill
c) Kelly is as tall as Jill d) It's impossible to tell


9. A boy is 4 years old and his sister is three times as old as he is. When the boy is 12 years old, how old will his sister be

a) 16 b) 20 c) 24 d) 28 e) 32



GSGE (9,4) =

9 - (((2 exp 6)-4)/3)

7) D
8) D
9) B
GSGE (9,4) - with bacon or sausage? (I must confess I cheated on this one. I thought GSGE was the name of some obscure function, so I Googled it.)

Mark:

7) D
8) D
9) B

"GSGE (9,4) - with bacon or sausage? (I must confess I cheated on this one. I thought GSGE was the name of some obscure function, so I Googled it.)"

You have come to the right place to ?'confess' what you say here will never be disclosed. :wink:
You did better than me, when I searched I got:


... gsge, shun shun shun shun shun good shun shun shun shun shun. issue issue issue issue issue issue issue issue issue issue, System Load ...

Now what do you want to say about Boston?



Francis:
9 - (((2 exp 6)-4)/3)

My dear Francis, please forgive my slowness, but I must ask; to which question does this answer appertain?




10. Assume that these two statements are true:

All brown-haired men have bad tempers.
Larry is a brown-haired man.
The statement Larry has a bad temper is:

a) True b) False c) Unable to determine


11. Two girls caught 25 frogs. Lisa caught four times as many as Jen did. How many frogs did Jen catch?

a) 4 b) 5 c) 8 d) 10 e) 15


12. Inept is the opposite of:

a) Healthy b) Deep c) Skilful d) Sad e) Happy


13. If all Zips are Zoodles, and all Zoodles are Zonkers, then all Zips are definitely Zonkers:

The above sentence is logically:
a) True b) False c) Neither e) Who cares

10) A
11) B
12) C
13) A

If Francis had written it like this:
9) (((2 exp 6)-4)/3)
it would have been the correct answer for 9.

As Mark said my answer was related to question 9.
A problem with the hyphen token for a minus.
(Flat joke?)