The worlds first riddle!

Drive in movie
Plan in action/plan of action

[size=8]CARS
After 1 billion trials, I get 2.742 which is close, but not close enough, to e.[/size]

Congratulations to Shari, our 5000th poster. Your place in history is assured.


Mark wrote:

"CARS
After 1 billion trials, I get 2.742 which is close, but not close enough, to e"

That is correct to three decimal places, I have a forth, but whose counting!


the MHIASKTOIRNYG


PPROISZET

[size=8]history in the making
prize in post?[/size]

Do you have a method (other than trials) for the car parking problem?

By the way, your activity in the never-ending story (and perhaps elsewhere) has enabled you to practically catch up to me in posts. I had been pulling away from you. I blame Shari. :wink:

Mark wrote, "Do you have a method (other than trials) for the car parking problem?"


I sure do, which I will post up tomorrow. I was found guilty at the trial, so I avoid them now.



We are now level on posts , you will have to up your work rate, I'm chasing Shari if only she would slow down.



CMARIRSKIS


LSHEARAID


RTARCYE

THMIRDAPLRACKE

[size=7]mark in crisis
shari in the lead
try in race
mark in third place[/size]

Shari:

MODRVIIVEE
Drive in movie

APCLTAIONN
Plan in action


Mark:

CARS
After 1 billion trials, I get 2.742 which is close, but not close enough, to e.


11/3 - 4/3*ln(2) = ~ 2.7425

Let f(x) denote the answer.
Let I(a,b) denote the integral from a to b. It is obvious that f(x)=0 for x<1.
It is obvious that f(x)=1 for 1<=x<2.
If 2<=x<=3 then f(x)=1+2*(x-2)/(x-1). This can be found by using simple geometry which is left for you to do.

Now lets solve x=4. The first car will divide the rest of the street into a small and a large portion, lets call them s and l. s is equally likely to range from 0 to 3/2. l is equally likely to range from 3/2 to 3. The probability that the smaller portion is less than 1 is 2/3. Likewise the probability that smaller portion is greater than 1 is 1/3. If the smaller portion is greater than 1 then exactly 3 cars will be able to park. If the smaller portion is less than one the number than will be able to park is 1+f(l).
f(x) = 1/3*3 + 2/3*(1+f(l), where l goes from 2 to 3)
= 1 + 2/3*(1 + I(2,3) 1+2*(x-2)/(x-1) dx)
= 1 + 2/3 + 2/3 + 4/3*I(2,3) (x-2)/(x-1) dx, next let y=x-1
= 1 + 4/3 * 4/3 * I(1,2) (y-1)/y dy
= 7/3 + 4/3 * I(1,2) 1 - 1/y dy
= 7/3 + 4/3 * (y-ln(y) for y from 1 to 2)
= 7/3 + 4/3 * (2-ln(2)-1+ln(1))
= 7/3 + 4/3 - 4/3*ln(2)
= 11/3 - 4/3*ln(2)
= ~ 2.7425

Better arrange valet parking!

the MHIASKTOIRNYG
history in the making


PPROISZET
prize in post

CMARIRSKIS
mark in crisis


LSHEARAID
shari in the lead


RTARCYE
try in race

THMIRDAPLRACKE
mark in third place


Over in Shari's apartment (don't ask me how I know) is a round table, which sits flush in a corner of a square room. One point on the edge of the table is 5" from one wall and 10" from the other.

What is the radius of the table



MUDASNCIEC


ASWTAAKYE

[size=8]TABLE
take your pick: 5" or 25"

dancing music
staying awake[/size]

You are to roll a die over and over until you get a six. What is the expected total of all throws before you throw a six

By the "total" I mean the sum of the die faces, for example the sequence 1-3-5-6 would have a total of 9.



BUBBBLLOEWS

blowin' bubbles.....??? Who's Bubbles???

bubbles is a clown!!!!!

Hiya Ralph, long time no see. Did you have a good holiday?

Bubbles was just clowning around.




TCRLOOUWBNLE

Yep! Got to hold my daughter for the first time. There was a camera crew from one of the local stations. After I had been cryin like a baby for 5 minutes my wife THEN informs me that we are on camera. They showed it that entire weekend. How sad is that to have a 6'+ 200lb+ soldier cryin like a 2 yo!



I loved every minute of it!

[size=8]ROLL A DIE
I'll guess 15.

clown in trouble[/size]

Mark:
TABLE
take your pick: 5" or 25"

Let the radius of the table be r.
Denote the corner of the room (0,0), the point of contacts (0,r) and (r,0) and the point on the edge in question (10,5).
Draw a triangle with these points (10,5), (r,5), and (r,r). This is a right triangle with sides of length r-10, r-5, and r. The Pythagorean formula tells us that (r-10)^2 + (r-5)^2 = r^2. Solving for r yields r=5 and 25.


ROLL A DIE
I'll guess 15.

How can you just guess the correct answer, life is so unfair.
Let x denote the answer on any given trial of this experiment.
Let E(x) denote the expectation of x, in other words the answer to this problem.

E(x)=(1+E(x))/6 + (2+E(x))/6 + (3+E(x))/6 + (4+E(x))/6 + (5+E(x))/6
E(x)=(15+5*E(x))/6
E(x)=15


MUDASNCIEC
dancing music

ASWTAAKYE
staying awake

TCRLOOUWBNLE
clown in trouble



Shari:

BUBBBLLOEWS
blowin' bubbles

Modesty forbids my further comment.


Ralph wrote;
"Yep! Got to hold my daughter for the first time. There was a camera crew from one of the local stations. After I had been cryin like a baby for 5 minutes my wife THEN informs me that we are on camera. They showed it that entire weekend. How sad is that to have a 6'+ 200lb+ soldier cryin like a 2 yo! I loved every minute of it!"


That is a most touching and joyous story, pure spontaneous emotion. My very best wishes to you all.




On average how often does the minute hand pass the hour hand on an ordinary clock



PCRAYIINGN


the RCAANDILEN

ROLL A DIE
I figured each of 1 through 5 was equally likely to be rolled before the 6. 1+2+3+4+5=15.

CLOCK HANDS
11/12 times per hour

crying in pain
candle in the rain (I've heard of candle in the wind, but not candle in the rain)

on average the second hand passes the minute hand once a minute

Mark wrote, "(I've heard of candle in the wind, but not candle in the rain)"


I'm not surprised, it was a short reign.



Ralph wrote, "on average the second hand passes the minute hand once a minute"

Buddy, you crack me up. You answer your own questions, makes an interesting puzzle, not sure about your answer.
(Keep your hand off the timer till we sort it out)





IRWAARQ


DCOOUNWTN


SIEGNHDT

[size=8]war in Iraq
counting down
end in sight[/size]