The worlds first riddle!

I am sure it is Mark, and as you say, he is flashing…

Is there anyone here? I have seen more action at a post mortem.


What is the expected number of flips of a fair coin until you get two heads in a row? What is the expected number until you get a head followed by a tail? Note: The answers are not the same.

Mark:

COIN FLIPS
two heads: 6 flips
head/tail: 4 flips

First lets answer the question of the expected number until you obtain two heads. There are two possible states, either the last flip was a heads (state x) or a tails (state y). The first flip is also in state y. From state x you have a 50% chance of going to state y and 50% of staying in state x. From state y you have a 50% chance of ending the experiment and a 50% chance of dropping back to state x. Now set up these statements in equation form and solve, call E(x) the expected number of future flips from state x and likewise for E(y) from state y:
E(x)=1 + (E(x)+E(y))/2
E(y)=1 + (E(x))/2
Solving for E(x) and E(y) yields E(x)=6 and E(y)=4. Since the first state is x the answer is 6.

Approach the second problem in the same way, however this time from state y you either end or stay in state y, thus the equations are:
E(x)=1 + (E(x)+E(y))/2
E(y)=1 + (E(y))/2
In this case E(x)=4 and E(y)=2, the answer being E(x) or 4.

Nice one Mark.


IMUR:

Total e+e+e+e +awe = totally awesome

>?
bigger question (I have pointed, but bigger is better)



You are standing on a rock in the middle of a circular lake of radius 1. There is a tiger on the shore of the lake that can run four times as fast you can swim, however the tiger can not swim. The tiger is hungry and always attempts to keep the distance between the two of you at a minimum. How can you safely swim to shore?

Shari:

Until you are more than 1/4 of the radius away from the rock you can swim fast enough so that you can stay 180 degrees away from the tiger. Regardless of which direction the tiger moves around the circle you swim the other way, always keeping 180 degrees away, and moving outward with leftover energy.

Before long you will be 1/4 of the radius away from the center and the tiger will be 180 degrees away. At this point, swim straight to the point on the shore furthest from the tiger. You will be able to get there in 3/4 units of time, while it will take the tiger pi/4 =~ 0.7854 units of time.
After that, you are on your own!

Way to go girl, I could not have put it better.


stayinggame


goaodtillme




It is your task to determine how high you can drop a billiard ball without it breaking.

There is a 100 story building and you must determine which is the highest floor you can drop a ball from without it breaking.
You have only two billiard balls to use as test objects, if both of them break before you determine the answer then you have failed at your task.

How can you determine the breaking point in which the maximum necessary dropping is at a minimum?

TIGER
You can safely swim to shore by taking any route. It's when you get to shore that you are eaten.

I've seen this before. It involves swimming in a spiral. I don't know the exact answer.

staying ahead of the game
all in good time ("my pretty, all in good time" - WW of the W)

BILLIARD BALL
been there, done that

Mark:
stayinggame
staying ahead of the game


goaodtillme
all in good time
( )


goaodtillme


Wwooolfl

[size=7]wolf in sheep's clothing[/size]

Whats up my handsome men? It looks like you have been getting along swimmingly without me.
I will be back later with some tricky ones.

The waving franticly of arms is not swimming, it's called drowning!

If you cant teach me to swim, please teach me to fly.

The Chompem Cannibals of Drybone Island have the annoying habit of eating each other. In fact, Grandpa Chompem went missing only last week, and it was thought he'd lost his way home until his bits and pieces were found on the beach. One evening, the Chompems threw a dinner party, one of those bring-a-friend get-togethers. Six cannibals turned up and they decided to eat each other in turn. So someone was selected for everyone to eat (except the victim!), and when he had been eaten, someone else was selected, and so on. If it took one cannibal two hours on his own to devour one person, how long was it before just one consumer remained?

"I've always been 45 years older than your Dad", said Grandma to young Trickle."But now the two digits in my age, both prime, are the reverse of the two in your Dad's age". How old is Grandma?

In the Dark Ages, in a remote part of Scotland, there once lived a 14-foot giant called Scrambo who used to terrorize the villagers by chasing them with his stick. They were so scared of him that when he ordered them to build a small castle for him to live in they quietly agreed. Fortunately for the villagers, Scrambo was rather stupid, and he chose flat land for his castle rather than the usual high ground. An annular moat was dug around a central circular region and the excavated soil was evenly distributed over the central region. There it was flattened to its original density to make a platform for the castle, raised above ground level. The buckets of soil were hauled from the moat with the aid of three wooden poles which spanned the moat .Each pole was three times the height of the giant and each just touched the central region and intersected another pole at the outer circumference of the moat.
The vertical distance D from the bottom of the moat to the top of the platform was exactly equal to that part of a pole spanning the moat. When one end of a pole was seated halfway across the flat moat bottom the other end just reached the top of the platform (i.e. the pole forms the hypotenuse of a right-angled triangle in a vertical plane, the height of which is D). What was the width and depth of the excavated moat?

As Sad Sally passes the town hall clock each day at noon, she looks at the clock and changes her watch to 12:00:00 (hours:minutes:seconds).She then goes home, and for want of something better to do, she listens out for the clock chimes. She believes that the single chime she hears at regular intervals occurs each hour on the hour and that since her watch must be wrong, she alters it accordingly. In reality, her watch runs at the same rate as the town hall clock, but the clock chimes on each occasion the hour and minute hands point in the same direction. What time is it on Sally's watch when she passes the town hall clock?

Did everyone go on effin' holiday or what?

"effin' holiday"

That sounds cute, where do Elf's go when they go on holiday?

This is one tough set, but I am willing to go first.

Gross Cannibals.
If it took five cannibals 2/5 hours to eat the first victim.
Four cannibals 2/4 hours to eat the second.
Three cannibals 2/3 hours to eat the third.
Two cannibals 2/2 hours to eat the fourth.
One cannibal 2/1 hours to eat the fifth.

[size=7]It therefore must have taken 4h. 34 minutes for the last cannibal to wash the dishes. [/size][size=7]Only 7.2 are both prime numbers.
Therefore, Grandma is 72 years young.[/size]

God you are good....I am calling your teacher to tell them how much you paid attention.

OMG don't do that - they will check the register and wonder why I have been skipping classes.

I would need a diagram to solve the castle problem. I can't picture how the three poles are arranged.

SAD SALLY
Every 12/11 hours, Sally sets her watch back 1/11 of an hour (to the nearest hour). At 10:54:32.7 a.m., she sets her watch to 9:00 a.m. Therefore, when she passes the clock at noon, her watch reads 10:05:27.3 a.m.

Mark wrote, "I can't picture how the three poles are arranged."


The question states, "an annular moat was dug around a central circular region"

I take this to mean; a ring (moat) with the soil piled on a circle. The three poles would have to form a triangle.

As the pole is given as 3x14=42 feet long and this must be 7r/2 then the radius r (the moat width) is 12 feet. The area of the full outer circle is four times that of the inner one (since the radius is 2r).

Therefore, the annulus area (an annulus; the Latin word for "little ring", is a ring-shaped geometric figure, or more generally, a term used to name a ring-shaped object. The area of such an annulus is given by the difference in the areas of a circle of radius R and one of radius r)Is three times the inner circle area.

This means that the soil dug up and piled onto the inner circle makes the height of the platform above the existing ground is three times its depth. The depth of the moat is then a quarter of the pole span.

If so, then the moat is 12 feet wide and 10.39 feet deep. We can find half the pole span thereby giving us the full pole span which equals the height of the platform. This in turn gives us the full length of the pole which is the hypotenuse.


Has anyone seen that freekin fairy, this is doing my headin.



ncontrolled bigtime


blood, , and tears.


You have two bags of m&m candy. One bag has 99 red candies and 1 blue candy.

The other bag has 99 blue candies and 1 red candy. You choose a bag at random, open it, and draw just one candy from the bag. If the candy drawn is red, what is the probability that it was drawn from the bag with 99 reds and 1 blue

I see. So we've got a circle (radius r) inscribed in an equilateral triangle and a circle (radius R) circumscribed about the same triangle.

R=2r, so width of moat is r
Area of annulus is three times the area of the inner circle. Therefore, for each foot of moat depth, the inner circle grows by three feet.
D=depth of moat
4D = depth of moat from top of inner circle

The length of pole (L) spanning the moat is the same as the diameter of a circle with the same area as the annulus (3*pi*r^2).
So, L = 2*sqrt(3)*r

4D = L
D = sqrt(3)*r/2

The right triangle info tells us that:
(4D)^2 + (r/2)^2 = 42^2
So,
12r^2 + (r^2)/4 = 42^2
r = 12
So, the width of the moat is 12 feet.
The depth of the moat is 10.39 feet.

This confirms Try's answer, but I don't know where his statement, "As the pole is given as 3x14=42 feet long and this must be 7r/2" comes from.

[size=8]no sweat

M&M
99/100[/size]

I still don't see where 7r/2 comes from.

[size=8]GLASSES
2^7 + 1 = 129 glasses
log2(128) = 7 and one more test for the 129th glass = 8 tests

smokin' kills[/size]

It took 4 hours 34 minutes for one cannibal to remain. It took 5 cannibals, 2/5 hours to eat the first victim, four cannibals 2/4 hours to devour the second, three cannibals 2/3 hours for the third, two cannibals 2/2 hours for the fourth and one cannibal 2/1 hours for the fifth. One could argue that stomach contents increase a cannibal's edible volume when he is the victim. However, if the further interpretation is granted that these contents also turn a cannibal as consumer into more than one cannibal, the original solution is restored!



Grandma was 72 years old. Let the two digits be A and B. Then 10A+B-10B-A=45 so 9(A-B)=45. This gives A-B=5. Of the pairs 5,0; 6,1; 7,2; 8,3; 9,4 only 7,2 are both prime numbers.


Here is a picture if this helps anyone.






The time on Sally's watch is 10:05:27am. Each time the minute hand rotates 360 degrees, the hour hand rotates 30 degrees. If x is the number of rotations of the minute hand between consecutive alignments, then 360x - 360 = 30x where the subtracted 360 occurs because x is greater than one. So the hands are in alignment every 12/11 rotations of the minute hand, there being 11 alignments every 12 hours. Sally keeps subtracting 1/11 hour off her time at each chime believing it occurs on the hour. There are 21 adjustments before Sally sees the clock again (at the 22nd alignment) so we need 24 minus 21/11 hours for the solution.

So I will wait to post the answer to #3 and give you time to look at the picture.