Math Forum / Mathematics / Recreational Math / March 2007

How many digits would on average be missing if you draw one digit D
times with replacement?
Accoring to the simple formula 0.9^Dx10 it would be 3.5 with a
std.dev. of 1. But I'm unclear about larger draws such as 22.

Recently I found an intersting triangle center, that can be viewed at the following URL
http://www.geocities.com/alfetc
Comments and discussions are welcome.
Best regards,

Something like this was used to explain quantum entanglement
in a book by Julian Brown called, Quest for the Quantum Computer:
A single black box has:
  an on-off switch,

find the coefficient of x^5 in (x-1)*(x^2-2)*(x^3-3)..............
(x^100-100)

1455 base 6 converts to 1103 base 7
1455 base 7 converts to 1103 base 8
1455 base 8 converts to 1103 base 9
...

Hello all computer algebra knights, ;)
None of the modern-generation computer algebra systems
can handle this limit straightforwardly
  limit(2^a*int(cos(ln(z))/(1+z^2)^a, z= 0..infinity),

[Sorry to sci.math - I meant to crosspost this to a.m.r. before.]
AMM Readers-
Does anyone else find Problem 11280 (in the current issue) kind of screwy?
I was about to describe why I think so, but I wish to limit public

Hello all the computer algebra buffs,
Most surprisingly, the current generation computer algebra
systems fail do calculate this integral directly
 int(1/sqrt(z^3-I*z^2+z-I), z= -infinity..infinity);

That is a book by Carl Linderholm that seems to be very out of print and
hard to find.
Does anyone know if the title is available as an ebook or something?

Good morning to all,
As the Beatles sang: with a little help from my friends.............
My previous puzzle, about the paper hat, got a surprising turn. The
solution I had in mind possibly can be surpassed. But in order to be

Hi everyone..i really need the answer to this problem so i would really appreciate it if you help me..THANKS
A spider is standing on vertex (S) in this cube. (The cube's 8 vertices’ are (S,A,G,B,E,D,C,F)
[img]http://www1.filehost.to/files/2007-03-20_03/195358_sss.jpg[/img]
The ...

Hello the computer algebra fans,
Using Maple/Mathematica operations, can you
calculate the exact value of this integral
  int(1/(1+cos(z)^10), z= 0..Pi);

While noodling around with a calculator, I noticed
the coincidence that 6/25 = .24, while 6/24 = .25.
Are there any more coincidences like this?
One way of looking at it is that we have two integer equations

Hello all the symbolic star girls and machos, ;)
None of the current generation computer algebra systems can
calculate this limit
 limit(int(z^a/(exp(z)-1)^a, z=0..infinity), a=infinity);

This problem is so simple, that it may be known already:
How to cut an A4 sheet of paper into 3 pieces,
which can be reassembled as a square?
Compasses and cm-ruler.