The worlds first riddle!

Oops! I jumped the gun.
That's for Try to determine. I'm stepping on toes.

Vimes:

Perhaps we should establish your gender up front so nobody makes any erroneous assumptions. And if you're a cute, young female, Try, no doubt, will want a photograph for verification. :wink:

Thanks for the welcome! As for my gender, it is summed up rather neatly by Chicago:

I'm a man, yes I am

Sorry Try :wink:

Maybe you already know it, maybe not:
11
21
1211
111221
What's next?

Hi Vimes, Is that; Commander Samuel (Sam) Vimes of Terry Pratchett's Discworld novels?

Anyways welcome, you are a ?'lurker' no more.



Vimes
The Ferries / river

The river is 1760 yards wide

Let the width of the river be x
The distances travelled by the 'right' ferry are x - 720 (first part) and 2x - 400 (total). The distances travelled by the 'left' ferry are 720 and x + 400. We now know that x - 720 : 720 = 2x - 400 : x + 400, or
(x - 720) / 720 = (2x - 400) / (x + 400)
x^2 - 320x - 288000 = 1440x - 288000
x^2 - 1760x = 0
x(x - 1760) = 0
x = 0 or x = 1760

Since 0 doesn't make sense, the width of the river is 1760 yards


?'Chicago' you say. What about Zao? Get with the programme.



Mark:

WHIM'S BOOK
220

If P(n) is the number of digits used to number n pages, the formula for P(n) is:
• P(n) = n , if n is between 1 and 9
• P(n) = 2n-9 , if n is between 10 and 99
• P(n) = 3n-108 , if n is between 100 and 999
• P(n) = 4n-1107 , if n is between 1000 and 9999
• P(n) = kn-[ (10k -1)/9 - k ] , if n is a k-digit number.
For the question at hand, we simply have to solve the equation 552=(3n-108) and that means that there are n=220 pages in the book. Or better still ask Mark.



RIVER
3*720 - 400 = 1760

Last edited by markr on Wed Sep 14, 2005 12:27 pm; edited 1760 times in total


Which is shorthand for saying; First, the time spent by the boats at their destination is irrelevant, as long as they both spend the same amount of idle time between each encounter. Ignore itLet u and v be the speeds of the boats and w the width of the river. Let a = 720 yd and b = 400 yd be the distances from the left and right shores given in the question. What we are told about the crossing points means that:

a / u = (w-a) / v
(w+b) / u = (2w-b) / v

Divide each side of the first equality by the corresponding side of the second equality and you obtain an equality where the speeds of the boats no longer appear, namely a/(w+b) = (w-a)/(2w-b), or rather a(2w-b) = (w-a)(w+b), which boils down to w = 3a-b (after ruling out w = 0 and dividing by w). The width of the river is therefore 3a-b = 1760 yds, or exactly 1 mile.


Vimes: You got it, and welcome.


If Mark says, "You got it" then you can be sure, you have really have got it. Congratulations.


Mark wrote, "Perhaps we should establish your gender up (front)"

Vimes replied, "I'm a man, yes I am"

To avoid any confidential information reaching the public domain, may I just confirm the gender issue from the medical records. Now put your clothes back on, and let battle commence. :wink:




Bo and Al, were trying out some new hot rod cars on the family's private race-track. Once both racers were up to their respective speeds (Bo's car was going 120 miles per hour, and Al's was going 95 mph), they crossed the starting Mark of the two-mile track just as the gun went off, and then maintained their respective speeds for 24 laps each.

At what position on the two-mile track (relative to the starting Mark) does this occur

Nopets Bonus: How much time passes until Bo first catches up to Al

Yes it is Try, good guess! Love Pratchett and love Vimes (and Rincewind, but that was taken already, besides Vimes seems appropriate in a riddle setting :wink: )

Having been a lurker here for a while, I wasn't too worried anymore about being wrong, after Mark had the same answer

Zao, you say? I honestly don't know them. Always nice to learn about a new band!

Something I've always wondered about (since you mention 1760 yards being 1 mile), what's the logic behind this? I know 12 Inch = 1 foot; 3 foot = 1 yard. Guess I'm indoctrinated with the decimal system :wink:

Vimes wrote, "good guess!"

Often have I said that when you have eliminated the impossible, whatever remains, however improbable, must be the truth. :wink:


"Something I've always wondered about…"

Now, that's a real riddle. Confused? You soon will be;

1 furlong = 10 chains (surveyors) = 660 feet = 1/8 statute mile = 201.168 meters
8 furlongs = 1 statute mile = 1,760 yards = 5,280 feet
80 chains = 1 survey mile = 320 rods = 5,280 feet
1 rod, pole, or perch = 16 1/2 feet = 5.029 meters
3 miles = 1 league = 5,280 yards = 15,840 feet


I have seen your question before; its good, but I will leave it to other enquiring minds.

I see you have already met Mark our resident genius, my life is spent keeping my toes out of his way.

Good to have you on the forum, have fun.

Thanks for the welcome again, Try :wink:

Here's a nice Pratchett quote "The British resisted decimalized currency for a long time because they thought it was too complicated", which obviously applies equally for decimalized distances

I had noticed Mark is a smart one! Let's hope he doesn't know the riddle yet and will find it a challenge!

[size=7][quote="Tryagain"] Bo and Al, were trying out some new hot rod cars on the family's private race-track. Once both racers were up to their respective speeds (Bo's car was going 120 miles per hour, and Al's was going 95 mph), they crossed the starting Mark of the two-mile track just as the gun went off, and then maintained their respective speeds for 24 laps each.

(1) At what position on the two-mile track (relative to the starting Mark) does this occur

(2) How much time passes until Bo first catches up to Al [/quote]

(1) At what position does what occur?

(2) Are you asking for the time it takes for Bo to lap Al if at time zero each is at the start and Bo is going 120mph and Al is going 95mph? If so, then 4.8 minutes.[/size]

Yeah - I've seen this several times before.

312211

You are, of course, correct. Too bad,you knew it already. Ah well.

Mark:

"Are you asking for the time it takes for Bo to lap Al if at time zero each is at the start and Bo is going 120mph and Al is going 95mph?"

Yes, that is exactly what I am asking, confident that the answer is so devilishly devious that a rational answer is all but impossible.


Mark:

If so, then 4.8 minutes.


Wait! If you will let me finish; …for anyone born after 2002.



Commander Sam Vimes wrote, "You are, of course, correct. ……... Ah well."

I think you will be using those words a lot round here. I have a bank of unused phrases such as;

?'Dream on sucker'
?'You wish'
?'No way'
?'Blow it out your $$$'

I have never been able to use….Ah well




The Kappa Kuppa K'rona fraternity was planning for the Big Bash. Usually, 10 cases of Spud Beer, which is 6 and 1/4 % alcohol by volume, are required for the Bash.

(There are four 6-packs per case, and 12 ounces per beer, of course!).

This year, however, crafty funds manager George Waldo Busch calculated that they wouldn't need to buy as many cases if they got "Beastie Beer" instead, since that brand has a mind-numbing 15 and 5/8% alcohol by volume.

How many cases of "Beastie Beer" should Busch Buy for the Big Bash


Do you know;


1. Which of the dwarves did not speak in Disney's "Snow White and the Seven Dwarves"

a-Dopey, b-Grumpy, c-Bashful, d-Doc.

2. What astronaut turned senator made three orbits of the Earth aboard the spaceship Friendship 7

a-Jake Garn, b-John Glenn, c-Alan Shepard Jr., d-Neil Armstrong.

3. What writer living in Salem, Mass., wrote a famous story about the local landmark "The House of the Seven Gables"

a-Washington Irving, b-Mark Twain, c-Nathaniel Hawthorne, d-Edgar Allan Poe.

4. Who created secret agent 007, aka James Bond

a-W. Somerset Maugham, b-Kenneth Grahame, c-Ian Fleming, d-Len Deighton.

5. What is the last remaining and oldest of the 7 Wonders of the Ancient World

a-Arc de Triomphe, b-The Great Pyramids, c-Hanging Gardens of Babylon, d-Stonehenge.


I have been reminded by 'Slim' that the following has NOT seen an answer.
(May I say I am not surprised, it is all but impossible)

In a "seven-eleven" (7-11) store, a customer selected four items to buy. The check-out clerk says that he multiplied the costs of the items and obtained exactly 7.11, the very name of the store! The customer calmly tells the clerk that the costs of the items should be added, not multiplied. The clerk then informs the customer that the correct total is also $7.11

What are the exact costs of the 4 items

[size=7]BEER
4

DO YOU KNOW
1. a
2. b
3. c
4. c
5. b[/size]

SEVEN ELEVEN
oops - I meant to get back to that - I will

[size=7]SEVEN ELEVEN
$1.20, $1.25, $1.50, $3.16[/size]

Question: What happens after death?

Answer : Nobody lived to answer that..


Nitin Dandriyal.

Question: What happens after death?

Answer : Nobody lived to answer that..


Nitin Dandriyal.

There's no escaping.... Grunt.


This one is .. for you Mark,

A girl took part in a (some) game with many others in a circular closed circuit. After pedaling for several minutes, she found that 1/3th of the cyclists ahead of her and 3/4th of the cyclists behind him together formed the total no. of participants. How many were participating in the race?

CYCLISTS
13

Mark:

BEER
4


96 Beers

16 Sixers

Or 4 Cases


DO YOU KNOW
1. a
2. b
3. c
4. c
5. b

1. a-Dopey.
2. b-John Glenn.
3. c-Nathaniel Hawthorne.
4. c-Ian Fleming.
5. b-The Great Pyramids.


SEVEN ELEVEN
$1.20, $1.25, $1.50, $3.16




There's only one possible solution, namely:
7.11 = 3.16 + 1.25 + 1.50 + 1.20 = 3.16 x 1.25 x 1.50 x 1.20

Proof :
If a, b, c, d are the prices of the items expressed in (whole) cents, what we are told is that a+b+c+d = 711 and abcd = 711000000 = 26 32 56 79.
So, one (and only one) of the amounts, say a, is a multiple of 79. This is, of course, less than 9 times 79 (which is 711), and may thus only be 1,2,3,4,5,6, or 8 times 79 (7 times 79 is ruled out, because it does not divide 711000000). These 7 possibilities translate into the following equations:

1. a=79, b+c+d=632, bcd=9000000
2. a=158, b+c+d=553, bcd=4500000
3. a=237, b+c+d=474, bcd=3000000
4. a=316, b+c+d=395, bcd=2250000
5. a=395, b+c+d=316, bcd=1800000
6. a=474, b+c+d=237, bcd=1500000
7. a=632, b+c+d=79, bcd=1125000

Now, the product of 3 positive numbers of given sum is greatest when they are all equal, which means that the product bcd cannot exceed (b+c+d)3/27. This rules out the last three of the above 7 cases.

In the first three cases, on the other hand, the sum b+c+d isn't a multiple of 5, so at least one of b,c,d (say d) isn't either. Therefore, the product bc must be a multiple of the sixth power of 5. Since neither b nor c can be large enough to be a multiple of the fourth power [625 is clearly too big a share of 711, leaving only 7 cents for two items in the first case and nothing at all in the other two] we must conclude that both b and c are nonzrero multiples of 125.

The number d would thus be obtained by subtracting from one of three possible sums (632, 553, 474) some multiple of 125 (necessarily: 250, 375 or [in the first two cases] 500). This gives only 8 possible values for d (382, 257, 132, 303, 178, 53, 224, 99). Each is unacceptable because it has a prime factor other than 2 or 3.

Therefore, only the fourth case is not ruled out, so that a=$3.16.
a=316, b+c+d=395, bcd=2250000.
Since the sum b+c+d is a multiple of 5, and at least one of the terms is a multiple of 5, either only one is, or all are. The former option is ruled out since this would imply for the single multiple of 5 to be a multiple of 56=15625, which would, by itself, be much larger than the entire sum of 395. So, b, c, and d are all multiples of 5, and we may let b=5b', c=5c', d=5d', where b'+c'+d'=79 and b'c'd'=18000.

Now, these three new variables may not be all divisible by 5 (otherwise their sum would be too). It's not possible either to have a single one of them divisible by 5, because it would then have to be a multiple of 53=125 and exceed the whole sum of 79. Therefore, we must have a multiple of 25 (say b'=25b") and a multiple of 5 (say c'=5c"): 25b"+5c"+d'=79 and b"c"d'=144. It is then clear that b" can only be 1 or 2. If b" was 2, then we would have 5c"+d'=29 and c"d'=72, implying that c" is a solution of x(29-5x)=72 or 5x2-29x+72=0. However, this quadratic equation does not have any real solutions, because its discriminant is negative. Therefore, b" is equal to 1 and b=5(25b")=125=$1.25.

The whole thing thus boils down to solving 5c"+d'=54 and c"d'=144, which means that c" is solution of x(54-5x)=144 or 5x2-54x+144=0. Of the two solutions of this quadratic equation (x=6 and x=4.8), we may only keep the one which is an integer. Therefore c"=6, c'=30, c=150=$1.50.

Finally, d'=144/c=24 which means d=5d'=120=$1.20.
Therefore, the solution is unique (the order of the 4 items being irrelevant). Well done Mark






Look at this sentence and see if you can find the reason why all the 2-letter words have a common trait. What is this trait

"Hi! Ma and Pa told me I'd better say that all the two-letter words in this sentence have something in common ..... or else!"





While Barb was out golfing with her husband George, they met Ron. Ron was Barb's only sister's mother-in-law's only son's grandfather in-law. What was Ron's relationship to Barb



A man left home one day and made three left turns and met a man with a mask on. What was the first man's profession



What number comes next in the following sequence

1/4, 1/2, 3/4, 1, 5/4, 3/2,




A quick math question: If all the numbers in existence starting with zero were written in English and then arranged in alphabetical order, what number would be first



The number 2002 reads the same backwards and forwards. (This is called a palindromic number). Name a palindromic number with an even number of digits




Welcome Nitin, are you related to Tintin? He was so good they named him twice.

You wrote, "Question: What happens after death?"

"Answer : Nobody lived to answer that.. "

I'm a nobody, and lived to tell the tale.
CYCLISTS
4

First the cricket and now the baseball!