The worlds first riddle!

Mark:


COYPU
1, 2, 6, 7, 9, 14, 15, 18, 20

I did write a program for this one.

Your programming skills are much to be admired



For each positive integer n, let A_n be the number of digits in the binary representation of n, and let B_n be the number of ones in the binary representation of n.
What is (1/2)^(A_1+B_1) + (1/2)^(A_2+B_2) + (1/2)^(A_3+B_3) + ...


This is much easier than it looks, especially if you already have the answer.

i don't have the exact answer...but i have another sequence
first i started writing the numbers down in binary....then i noticed the exponents would make rows of pascal's triangle....and then the multiplicity of the exponents would make fibonacci's sequence:
the sum is equal to:
(0)1/2^1 + (1)1/2^2 + (1)1/2^3 + (2)1/2^4 + (3)1/2^5 + (5)1/2^6 + (8)1/2^7 + (13)1/2^8 + (21)1/2^9..... where the numbers muliplying the exponents make fibonacci's sequence 0 1 1 2 3 5 8 13 21...
im thinking the sum tends to 1.

[size=8]BINARY
It equals

SUM{n = 1 to infinity, F(n)/[2^(n+1)]}

where F(n) is the nth Fibonacci number.

I can't prove it, but it converges to 1.[/size]

Thoh:

I don't have the exact answer...but i have another sequence
first i started writing the numbers down in binary....then i noticed the exponents would make rows of pascal's triangle....and then the multiplicity of the exponents would make fibonacci's sequence:
the sum is equal to:

(0)1/2^1 + (1)1/2^2 + (1)1/2^3 + (2)1/2^4 + (3)1/2^5 + (5)1/2^6 + (8)1/2^7 + (13)1/2^8 + (21)1/2^9..... where the numbers muliplying the exponents make fibonacci's sequence 0 1 1 2 3 5 8 13 21... im thinking the sum tends to 1.



Mark:

BINARY
It equals

SUM{n = 1 to infinity, F(n)/[2^(n+1)]}

where F(n) is the nth Fibonacci number.

I can't prove it, but it converges to 1.



You guys are far too smart, try answering with one hand tied behind your back.


Note that A_{2n} + B_{2n} = A_n + B_n + 1 and A_{2n+1} + B_{2n+1} = A_n + B_n + 2 and so letting S = (1/2)^(A_1+B_1) + (1/2)^(A_2+B_2) + ... we see that S = 1/2^2 + (1/2)^(A_2+B_2) + ... = 1/2^2 + (1/2 + 1/2^2)*((1/2)^(A_1+B_1) + ... and so S = 1/2^2 + S*(1/2 + 1/2^2). It follows that S/4 = 1/4 and therefore S=1.




Another slice of pi:


In 1949, a digital computer was first used to calculate pi. To how many decimal places was this computer, ENIAC (Electronic Numerical Intergrator and Computer), able to find pi (would you believe it took 70 hours)

o A. 10,493
o B. 576
o C. 2037
o D. 8331
o E. 297,454



Answer the following question (an example of pi's importance in probability), posed and solved by George Louis Leclerc, Comte de Buffon (solved also nowdays by many students in introductory statistics classes):

Let a needle of length L be thrown at random onto a horizontal plane ruled with parallel lines spaced by a distance d (greater than L) from each other. What is the probability that the needle will intersect one of these lines

o A. pi*d^2
o B. pi*d*L
o C. 3d/(pi*L)^2
o D. 2L/(d*pi)
o E. e^(pi*i*d*L)


What is the value of e^(i*pi)

o A. the square root of -1
o B. approximately 10
o C. pi squared
o D. -1
o E. 1.414


What is the earliest known reference to pi

o A. the Rosetta Stone, inscribed in approximately 200 BC
o B. a Middle Kingdom papyrus scroll, written around 1650 BC by Ahmes the scribe
o C. Euclid's Elements, written in the 3rd century BC
o D. The Uselessness of Pi and its Irrational Friends, written in 1994 AD
o E. the Bible

[size=8]PI QUIZ
The only one I know without looking up is #3 (D).[/size]

It's only a bit of fun to see how close you can get with a guess; no one could be expected to know all the answers.

[size=8]PI QUIZ
(1) B (because it's the smallest number)
(2) D (it's the only one where 0 <= p <= 1)
(3) see previous post
(4) B (because it's the earliest)[/size]

Mark:

PI QUIZ

(1) B (because it's the smallest number)
(2) D (it's the only one where 0 <= p <= 1)
(3) The only one I know without looking up is #3 (D).
(4) B (because it's the earliest)


1.= C. 2037






Marlborow Million dollar contest questions
(The ones they did not want you to see)


I am periodically #79. They once tried to make me from # 29. If you add me to # 80, I will appear to be # 47 temperature.

What am I


Why does milk from the fridge not taste as cold as water or pop in the fridge


Why do blacktop roads get lighter in colour as they age

[size=8]CONTEST QUESTIONS
gold
fat content (guess)
oxidation (guess)[/size]

The BIG weekend crossword:

You will need to determine the numbers for each of the "trivial" calculations labeled A through Y. (5x5) Then you will need to perform each calculation and enter the answer in the corresponding box.

The * represents the multiplication operation and the / represents division, + and -.

Each number from 1 to 25 will be used just once.

When all the boxes are correctly filled in, every row, every column, and the two diagonals will all add up to the same sum (the MAGIC NUMBER!). Once you've determined the magic number by filling in five boxes in a row, you'll have a clue toward filling in the other boxes.

ABCDE
FGHIJ
KLMNO
PQRST
UVWXY


CLUES:

A. Baseball Team + Notes in an Octave
B. Disciples * Gentlemen of Verona
C. Dave Clark ____ - Horsemen of the Apocalypse
D. Octopus' arms + Diagonals in a Triangle
E. Baker's Dozen + Couple
F. Books in the Old Testament - "Sweet _____"
G. Legs of a Bovine + Eyes of a Cyclops
H. Ounces in an Avoirdupois Pound - The Muses
I. Snow White's Dwarfs + "The _____ Seas"
J. Books of the Bible - Golden Anniversary
K. Degrees in a Circle / Degrees in a Right Angle
L. Dozen and a Half - Signs of the Zodiac
M. Ammendments in the Bill of Rights + Triangle's Sides
N. Octogenarian / Pecks in a Bushel
O. Human Adult's Teeth - One Decade
P. The Senses + The Great Lakes
Q. Months in a Year + Degrees Freezing (in Celsius)
R. Original Colonies + Sides of a Hexagon
S. Wonders of the World * "_____ Dog Night"
T. Known Planets / Feet in a Yard
U. "Dinner at _____" + The R's
V. Wilson's Points + Bits in a Half Dollar
W. Pentagon's Sides * Diagonals in a Pentagon
X. Booth Tarkington Book - Men On a Dead Man's Chest
Y. The Commandments - Dots in a semi-colon


So whats the magic number

[size=8]MAGIC NUMBER
How's this for magic? I'll tell you the magic number before solving even one of the clues. The magic number is 65.[/size]

[size=8]A. 9 + 8 = 17
B. 12 * 2 = 24
C. 5 - 4 = 1
D. 8 + 0 = 8
E. 13 + 2 = 15
F. 39 - 16 = 23
G. 4 + 1 = 5
H. 16 - 9 = 7
I. 7 + 7 = 14
J. 66 - 50 = 16
K. 360 / 90 = 4
L. 18 - 12 = 6
M. 10 + 3 = 13
N. 80 / 4 = 20
O. 32 - 10 = 22
P. 5 + 5 = 10
Q. 12 + 0 = 12
R. 13 + 6 = 19
S. 7 * 3 = 21
T. 9 / 3 = 3 (outdated)
U. 8 + 3 = 11
V. 14 + 4 = 18
W. 5 * 5 = 25
X. 17 - 15 = 2
Y. 10 - 1 = 9[/size]

Ok! So we don't got no SUV drivers here, what about…


Gently place; two Aces, 2 Kings, 2 Queens, and 2 Jacks anywhere in a 4x4 grid so that:

• Every Ace borders a King.
• Every King borders a Queen.
• Every Queen borders a Jack.
• No two of the same cards border each other.
• No Ace borders a Queen.

Border means horizontal or vertical.

Some say it's impossible, what's your take on it

A|K|Q|J
J|Q|K|A

Damn! I mean congratulations, your answers do indeed comply with the stated restrictive covenants. Needless to say that is not what I intended, the wording needs more work. However, due to this unforeseen consequence may I welcome Chiso. Have you been sent to Riddles as some form of punishment due in part to a recent transgression, or are you just on your way to the washroom?

While the A2k lawyers ponder the legal implications of an admission in part, what about two classics from the crypt:

A murderer is condemned to death. He has to choose between three rooms. The first is full of raging fires, the second is full of assassins with loaded guns, and the third is full of lions that haven't eaten in 3 years.

Which room is safest for him



A Father, son and grandson are walking in the park. A cop approaches them and asks for their ages. The Father replies, "My son is as many weeks as my grandson is in days, and my grandson is as many months old as I am in years. We are all 100 years together."

How old were each

[size=8]A room with dead lions is the safest.

5, 35, 60[/size]

Mark:

A room with dead lions is the safest.

5, 35, 60



Assume that you have just heard of a scandal and that you are the first one to know. You pass it on to 4 persons in a matter of 30 minutes. Each of these 4 persons in turn passes it to 4 other persons in the next 30 minutes and so on.

Assume that no one hears it more than once and that the world population is 5.6 billion.

How long will it take for everybody in the world to get to know the scandal



What is the smallest number which when divided by 10 leaves a remainder of 9, when divided by 9 leaves a remainder of 8, when divided by 8 leaves a remainder of 7, when divided by 7 leaves a remainder of 6, and so on until when divided by 2 leaves a remainder of 1

Rumor: 8 hrs.
1 + 4 + 4^2 + 4^3 + 4^4 + ... + 4^n = 5.6 x 10^9
the sum is approximately 4^n / (1-1/4) = 5.6 x 10^9
solving for n, n = 15.98 ~ 16
every even power of 4 takes 1 hr so 16/(1hr/30min)=16/2=8hrs