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Driveway
08-30-2002, 08:03 PM
Post your riddles and math/logic problems here

riddle:

Which word in the English language becomes shorter when it is lengthened?

moi
08-30-2002, 08:05 PM
short

Driveway
08-30-2002, 08:08 PM
Yea, you got any?
another riddle:
Must Get Here Must Get Here Must Get Here

MethodMan
08-31-2002, 09:41 AM
3 Mustketeers?

I dont know any riddles.

Driveway
08-31-2002, 09:43 AM
A barrrel weighs 20 pounds. A man puts something in it, and now it weighs less than 20 pounds What did he put in it.

Nick
08-31-2002, 10:00 AM
A burning match.

Driveway
08-31-2002, 10:04 AM
That good be, but not the answer I'm looking for

jdinger
08-31-2002, 10:19 AM
Oh, I know!

An anti-gravity field modulator!

Driveway
08-31-2002, 10:23 AM
No
Hint;
Starts with an H

Nick
08-31-2002, 10:24 AM
He but I suppose you would need alot of that for 20lbs.

Jet_Master
08-31-2002, 01:21 PM
a hole. duh

Aran
08-31-2002, 02:30 PM
if a it took a man 5 hours to dig 14 holes, how long would it take him to dig half of a hole?

-KEN-
08-31-2002, 03:31 PM
you can't dig half a hole.

Xterria
08-31-2002, 08:18 PM
approximatly 0.18 hours

really

Driveway
08-31-2002, 08:19 PM
Like Ken said, you can't dig half a hole

moi
08-31-2002, 08:23 PM
why not

Driveway
08-31-2002, 08:25 PM
As soon as you take some dirt out it's a whole hole

Aran
08-31-2002, 08:27 PM
yup, that's the right answer ken and drive.

Driveway
08-31-2002, 08:30 PM
See, I'm not completly stupid.
Riddle: (easy one)
The Pope has it but he does not use it. Your father has it but your mother uses it. Nuns do not need it. Your lady friend's husband has it and she uses it. What is it?

moi
08-31-2002, 08:45 PM
Originally posted by Driveway
See, I'm not completly stupid.
Riddle: (easy one)
The Pope has it but he does not use it. Your father has it but your mother uses it. Nuns do not need it. Your lady friend's husband has it and she uses it. What is it?

a penis.

Driveway
08-31-2002, 08:47 PM
Better than the real answer, but no

BMJ
09-01-2002, 12:25 AM
My riddle: (I gave up on the other one)

A hunter sets out from camp at 4 o'clock in the morning with a compass. According to the compass, he travels due south for 4 hours. At that time he sees a bear and kills it (he is a hunter after all). He drags the bear with him for 4 hours due east, and he takes a quick break. Then he drags the bear due north for 4 hours at which time he arrives back at his camp where he decides he doesn't want the bear after all, packs his SUV and leaves.

So what color was the bear that he killed?

Driveway
09-01-2002, 06:09 AM
white

golfinguy4
09-01-2002, 01:52 PM
What has been done by every male, except for one? Normally does it with many, but can do it by herself. Is world-renowned for her infinite skill and great noise. And gives many great pleasure.

P.S. You'll probably never get this.

rahaydenuk
09-02-2002, 01:54 PM
Well here's a maths one (quite easy):

By considering the series,

1 + t + t^2 + t^3 + ... + t^n

sum the series,

1 + 2t + 3t^2 + 4t^3 + ... + nt^(n-1)

for t not = 1, where a^b denotes a raised to the bth power.

Have fun!

Nick
09-02-2002, 10:33 PM
Good problem!
I think it's

(n * t^(n+1) - (n + 1) * t^n + 1) / (t-1)^2
I even sort of proved it.

rahaydenuk
09-03-2002, 03:17 AM
Originally posted by Nick
Good problem!
I think it's

(n * t^(n+1) - (n + 1) * t^n + 1) / (t-1)^2
I even sort of proved it.

Yeah that's correct, but where's the proof??

Nick
09-03-2002, 08:43 AM
This is how I found the answer

1 + t + t^2 + t^3 + ... + t^n
+ t + t^2 + t^3 + .... + t^n
+ t^2 + t^3 + ... + t^n
+ t^3 + ... + t^n
....
+ t^n

This I proved this was equal to
1 + 2t + 3t^2 + 4t^3 + ... + nt^(n-1)

After that I solved the sums and then used induction

rahaydenuk
09-03-2002, 09:01 AM
Originally posted by Nick
This is how I found the answer

1 + t + t^2 + t^3 + ... + t^n
+ t + t^2 + t^3 + .... + t^n
+ t^2 + t^3 + ... + t^n
+ t^3 + ... + t^n
....
+ t^n

This I proved this was equal to
1 + 2t + 3t^2 + 4t^3 + ... + nt^(n-1)

After that I solved the sums and then used induction

I see, well done, but I have a much shorter proof, using 1 + t + t^2 + t^3 + ... + t^n. Can you/anyone else find it?

You'll kick yourselves...

Good Luck!

Nick
09-03-2002, 09:30 AM
I noticed that derivative
of 1 + t + t^2 + t^3 + ... + t^n
is the 0 + 1 + 2t + 3t^2 +... + nt^(n-1)
I'm sure you could give a prove or solve it some how
using this?

rahaydenuk
09-03-2002, 09:37 AM
Originally posted by Nick
I noticed that derivative
of 1 + t + t^2 + t^3 + ... + t^n
is the 0 + 1 + 2t + 3t^2 +... + nt^(n-1)
I'm sure you could give a prove or solve it some how
using this?

Exactly! Well done.

If you sum the first series, using the standard geometric series result, you can then differentiate that result to get the sum of the second series, which is the same answer as you got.

Like this:

Summing first series (using standard geometric series result):

1 + t + t^2 + ... + t^n = (1 - t^(n+1))/(1 - t)

d(1 + t + t^2 + ... + t^n)/dt = 1 + 2t + 3t^2 + ... + nt^(n - 1)

Which implies that:

1 + 2t + 3t^2 + ... + nt^(n - 1) = d((1 - t^(n+1))/(1 - t))/dt
= (1 - t^n + nt^(n + 1) - nt^n)/((1 - t)^2)

I think that's quite a nice little solution...

Nick
09-03-2002, 10:26 AM
If you havn't got it already check out
concrete mathematic --- A foundation for computer science.
Lots of neat problems, most of them are solved in the back
of book.

I'm trying to read this book in my spare time, but I have
lots of course work so I havn't gotten too far. It's tough