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.

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.

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!

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.

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