The worlds first riddle!

0.164134697 is the probability that the 26 balls end up in different (26) containers. There are C(B+C-1,B) ways to distribute B indentical balls in C different containers. There are C(C,B) ways to select B containers. There is only one way to distribute the B balls in the B containers since they are identical. According to Excel, C(360,26)/C(385,26) = .164134697.

EXEL
Normal

Any goods in this shop that may be carried away are not on (for) sale.

No acrobatic feat that involves turning a quadruple somersault is ever attempted there.

I think the answer to Whim's question is the expected number of containers that contain balls. This would be calculated by summing the products of N and the probability associated with N. Think of this as a game. You toss 26 balls into an array of 360 containers. You will be paid $1 for each container that contains at least one ball. What is the expected value of the game? It turns out to be a bit over 24.

Mark wrote, "I think the answer to Whim's question is the expected number of containers that contain balls."

In which case, your answer will stand the test of time. I assumed, and assumption is a dangerous foundation onto which to build a solution. That all the balls will find containers. However, how many will have more than one. Still, it is not the first time that I must Tryagain.


"Any goods in this shop that may be carried away are not on (for) sale."
I have, ?'No goods in this shop, that are still on sale, may be carried away.'

No acrobatic feat that involves turning a quadruple somersault is ever attempted there.

EXEL
Normal

An Explanation
A Knight cannot make the statement "I'm no Knight", since this would be a lie and a Knight always tells the truth. A Knave could also not make the statement, since that would be a true statement, and a Knave never tells the truth. A Normal however can say "I'm no Knight". It's true, and Normals sometimes tell the truth.



In a city called Voven the following facts are true:
No two inhabitants have exactly the same number of hairs.
No inhabitant has exactly 40360 hairs.
There are more inhabitants than there are hairs on the head of any one inhabitant.

What is the largest possible number of inhabitants of Voven
(knowing that the number of inhabitants is not infinite)


It is dark in my bedroom and I want to get two socks of the same color from my drawer, which contains 24 red and 24 blue socks. How many socks do I have to take from the drawer to get at least two socks of the same color


As you know, the world population is growing very fast. The main cause is of course that a lot of babies are born.

How many babies are born every minute worldwide (approximately)


1. Nobody, who really appreciates Beethoven, fails to keep silence while the Moonlight-Sonata is being played;
2. Guinea-pigs are hopelessly ignorant of music;
3. No one, who is hopelessly ignorant of music, ever keeps silence while the Moonlight-Sonata is being played.


1. Coloured flowers are always scented;
2. I dislike flowers that are not grown in the open air;
3. No flowers grown in the open air are colourless.


1. Showy talkers think too much of themselves;
2. No really well-informed people are bad company;
3. People who think too much of themselves are not good company.

VOVEN
40360

SOCKS
3

Guinea-pigs don't appreciate Beethoven.
All flowers grown in the open air are scented.
Showy talkers are not really well-informed people.

Mark continues to amaze.



VOVEN
40360


An Explanation
To prove that the largest possible number of inhabitants of Voven is 40360, we first prove that Voven can have 40360 inhabitants, and secondy that Voven cannot have a larger number of inhabitants.
Assume that Voven has 40360 inhabitants, and that the inhabitants are numbered from 0 up to 40359. Further, assume that the number of hairs of each inhabitant is equal to his/her number. Then all three mentioned facts about Voven are true. So it is possible that Voven has 40360 inhabitants.

Now assume that Voven has more than 40360 inhabitants. Number them again from 0 onwards. And assume that the number of hairs of each inhabitant is equal to his/her number, except for inhabitant 40360 (because of the second fact). Now, whatever number of hairs this inhabitant 40360 has, it always violates either the first or the third fact. So Voven cannot have more than 40360 inhabitants.


SOCKS
3

Guinea-pigs don't appreciate Beethoven.
All flowers grown in the open air are scented.
Showy talkers are not really well-informed people.



Given the mathematical set N of natural numbers (0, 1, 2, 3, 4, 5, ...) and the set Z of integer numbers (..., -3, -2, -1, 0, 1, 2, 3, 4, ...).

Which of the following sentences is true

N has less numbers than Z
N has as many numbers as Z
N has more numbers than Z



The year is divided into four seasons: spring, summer, autumn and winter. On the northern hemisphere it is summer when it is winter on the southern hemisphere, and the other way around.

Which of the following sentences is true

The summer on the northern hemisphere is longer than the summer on the southern hemisphere

The summer on the northern hemisphere is shorter than the summer on the southern hemisphere

The summer on the northern hemisphere is as long as the summer on the southern hemisphere



1. No boys under 12 are admitted to this school as boarders;
2. All the industrious boys have red hair;
3. None of the day-boys learn Greek;
4. None but those under 12 are idle.


1. The only articles of food, that my doctor allows me, are such as are not very rich;
2. Nothing that agrees with me is unsuitable for supper;
3. Wedding-cake is always very rich;
4. My doctor allows me all articles of food that are suitable for supper.


1. No discussions in our Debating-Club are likely to rouse the British Lion, so long as they are checked when they become too noisy;
2. Discussions, unwisely conducted, endanger the peacefulness of our Debating-Club;
3. Discussions, that go on while Tomkins is in the Chair, are likely to rouse the British Lion;
4. Discussions in our Debating-Club, when wisely conducted, are always checked when they become too noisy.

The summer on the northern hemisphere is as long as the summer on the southern hemisphere.

cardinality of N = cardinality of Z = cardinality of Q (rational numbers)

N can be mapped to Z by
If N is even, Z = N/2
If N is odd, Z = -(N+1)/2

Z can be mapped to N by
If Z is negative, N = -2Z-1
If Z is non-negative, N = 2Z

All of the boys learning Greek have red hair.
Wedding cake doesn't agree with me.
Discussions, that go on while Tomkins is in the Chair, endanger the peacefulness of our Debating-Club.

Sorry Merlin, don't give up your day job. :wink:


The Solution: The summer on the northern hemisphere is longer than the summer on the southern hemisphere

An Explanation
The summer on the northern hemisphere, which lasts from the summer solstice (21 June) until the autumnal equinox (23 September), has an approximate length of 93.6 days. The winter on the northern hemisphere (and so the summer on the southern hemisphere), which lasts from the winter solstice (21 December) until the vernal equinox (21 March), has an approximate length of 89.0 days.



Mark, "cardinality of N = cardinality of Z"

The Solution: N has as many numbers as Z

An Explanation
Two sets A and B have the same number of elements if and only if there exists a so-called bijective function f from A to B.
Define the bijective function f: N -> Z as follows:
f(n) = -½n for n even
= ½(n + 1) for n odd
So for example, f(0) = 0, f(1) = 1, f(2) = -1, f(3) = 2, f(4) = -2, f(5) = 3 etcetera. f is a bijective function from N to Z, and therefore N and Z have the same number of elements.

All of the boys learning Greek have red hair.
Wedding cake doesn't agree with me.
Discussions, that go on while Tomkins is in the Chair, endanger the peacefulness of our Debating-Club.


Mark, thank you for the insight into ?'a stitch in time'




The calendar that we use has a name. What is the name of our western calendar



In our western calendar, there are years of 365 days and leap years of 366 days. How often is it a leap year in our calendar (Think!)


The earth not only orbits around the sun, but also spins round her axis. How long does one complete turn of the earth round her axis take



1. All my sons are slim;
2. No child of mine is healthy who takes no exercise;
3. All gluttons, who are children of mine, are fat;
4. No daughter of mine takes any exercise.


1. Things sold in the street are of no great value;
2. Nothing but rubbish can be sold for a song;
3. Eggs of the Great Auk are very valuable;
4. It is only what is sold in the streets which is really rubbish.


1. No books sold here have gilt edges, except what are in the front shop;
2. All the authorized editions have red labels;
3. All the books with red labels are priced at 5c. and upwards;
4. None but authorized editions are ever placed in the front shop

CALENDAR
Gregorian
397/400 years
23h 56m 4s

None of my sons are gluttons.
No daughter of mine is healthy.

Eggs of the Great Auk cannot be sold for a song.

All books sold here with gilt edges are priced at 5c and upwards.

Whim, you are a poet, but don't yet know it.

I-I+V-V=0
II-I-V-V=1
II-I IV-V=2
II-I III-V=3
III-I III-I=4
III+III-I=5
III+II+I=6
IIIXII+I=7
IIIXIII-I=8

Mark:

CALENDAR
Gregorian

23h 56m 4s

An Explanation
A year equals 365.2422 days. If the earth did not move around the sun, then the earth would make 365.2422 turns round her axis in one year. However, because the earth also makes exactly one orbit around the sun in that year, the earth makes 365.2422 + 1 = 366.2422 turns round her axis in one year. One turn therefore takes
365.2422 × 24 hours / 366.2422 = 23 hours, 56 minutes and 4 seconds.


397/400 years

An Explanation
In our western calendar every year of which the number is divisible by 4 is a leap year, except century years not divisible by 400. For example, the years 1700, 1800 and 1900 were no leap years, but the year 2000 was. Therefore, not every fourth year is a leap year.


CALENDAR
Gregorian


An Explanation
In 45 B.C. Julius Caesar replaced the Roman calendar by the Julian calendar. In 1582 A.D. pope Gregory XIII replaced the Julian calendar by the Gregorian calendar, by improving the leap year rule. This Gregorian calendar is the calendar we still use today. The International calendar is one of the many proposals that have been done for the 'improvement' of the Gregorian calendar.

I will get back to you when I can confirm your last post. Although on past form they will be A1.



A certain farmer has 100 hens, numbered from 1 up to and including 100. Only the hens with the numbers 13 up to and including 48 each lay one egg.

How many of the hens have not laid an egg

HENS
The simple answer is 64. However, does "each lay one egg" mean the rest don't lay any eggs, or the rest lay more than one egg?

Ooooh. Featured status!

Mark writes, "Ooooh. Featured status!"

May I thank all who have made a contribution to this depository of Riddle lore. Your names will be linked to this reference until the end of time. Anybody can set a question. However, it takes someone just that bit special to answer.
Also a word of thanks to all those behind the scenes who do so much to provide this great site. Enjoy


"The simple answer is 64."

The ?'simple' answer will do nicely.


Eggs of the Great Auk cannot be sold for a song.

All books sold here with gilt edges are priced at 5c and upwards.

All gluttons, who are children of mine, are unhealthy.




1. Remedies for bleeding, which fail to check it, are a mockery;
2. Tincture of Calendula is not to be despised;
3. Remedies, which will check the bleeding when you cut your finger, are useful;
4. All mock remedies for bleeding are despicable.
5.


1. None of the unnoticed things, met with at sea, are mermaids;
2. Things entered in the log, as met with at sea, are sure to be worth remembering;
3. I have never met with anything worth remembering, when on a voyage;
4. Things met with at sea, that are noticed, are sure to be recorded in the log.
5.


1. The only books in this library, that I do not recommend for reading, are unhealthy in tone;
2. The bound books are all well-written;
3. All the romances are healthy in tone;
4. I do not recommend that you read any of the unbound books.
5.





The numbers one through seven are drawn from a hat without replacement. What is the probability that all the odd numbers will be chosen first


Two candles have equal lengths. One is consumed uniformly in four hours, the other in five hours. If they are lighted at the same time, in how many hours will one be three times as long as the other

NUMBERS
1/35

CANDLES
3.5 hours

1. The only books in this library, that I do not recommend for reading, are unhealthy in tone;
2. The bound books are all well-written;
3. All the romances are healthy in tone;
4. I do not recommend that you read any of the unbound books.
5. All the romances are well-written.

Mark writes:

NUMBERS
1/35

CANDLES
3.5 hours

Works for me. However, I have ?'lost' the explanation for the time being.



Merlin writes, "5. All the romances are well-written." They sure are.



Whim writes:

"Can you, starting from the above sum, and replacing just one match each time make sums whose results are in succession 0 , 1, 2, 3, 4, 5, 6, 7 and 8?"

"where you had to reposition one match each time to get from 0 to 9. "


What I find very interesting, is the fact that starting from the same point, 7 and 8 were the same. All the rest are different. Very good problem though.



What is taller sitting than standing


Said the young girl, "My name is Elizabeth, and my
Grandmother has the same name. I am named after her,
But I know it to be true that she was just named after me.
The girl is telling the truth. How is this possible



1. No birds, except ostriches, are 9 feet high;
2. There are no birds in this aviary that belong to anyone but me.
3. No ostrich lives on mince-pies;
4. I have no birds less than nine-feet high.
5.

1. A plum-pudding, that is not really solid, is mere porridge;
2. Every plum-pudding, served at my table, has been boiled in a cloth;
3. A plum-pudding that is mere porridge is indistinguishable from soup;
4. No plum-puddings are really sold, except what are served at my table.
5.


Fake farmer woke up one morning to pandemonium in his barnyard. The gate had been left open and the animals had wandered out during the night. When he looked out the window, he could see the chickens and the sheep. By the time he got downstairs he could see the goats, too. But he had to hunt for the cows and the horses. After an hour of running around, Fake finally got all his animals back in their pens.

Using the clues below, determine how many of each animal the farmer had to find, what kind of mischief each type of animal got into, and how long it took the farmer to return each group of animals to their pens.

The animals running loose on the neighbour's lawn were not the goats.

The twelve chickens, who were not eating Fake's vegetable garden, took the most time to return to their pen.

Fake had five of one type of animal; he had an even number of all the other animals.

The animals he had the least number of were the ones found in the grain room.

The animals he had the most of took him twenty minutes to catch.

The animals Fake had only two of took five minutes to catch while the animals he had six of took twice as long to catch.

Fake had six more chickens than goats but two more goats than sheep.

It took five minutes more to catch the horses than it took to catch the animals in the hay field but getting the horses took five minutes less than collecting the animals scattered around the barnyard.

It took Fake the same amount of time to collect the four animals in the hay field as it did to collect the goats.

Thanks, but your solution starts with multiple match repositions, where only one was allowed. Later on I found that to 9 was possible too.

whim