Math Forum / Mathematics / Recreational Math / January 2005

Triangle ABC with B as a right angle has another triangle BDC fitted
inside with D as a right angle. If AB,BC,CA,BD,DC and AD are all
integers, and also all areas to be integers what is the smallest area
possible for ABDC?. Or for area ABC ?

Hi!  (FYI, I am the Mathcounts coach who hasn't taken math in 35 years.  I
am successful but only because I have others like you to ask.  Thanks!)  My
team had their last match before "the big one" today.  We won and we had the
1st and 3rd place scoring individuals overall.  I am ...

Suppose that all roots x_1,x_2,...,x_5 of polynomial
f(X)=X^5 - 10X^4 + 25X^3 + AX^2+ BX+ C
are real. Prove/or disprove/ that
4.915 < max_k{x_k} - min_k{x_k} < 7.746 .

How many squares can you make with this image?
each square must have for dots, one on each vertice
http://gape.ist.utl.pt/puzzles/images/sem18-a.jpg
If you find the answer reply to my e-mail please

I found out that there is a Buffon Laplace Needle Problem which says that
if you drop a needle of length l on a grid of squares who's dimensions are
aXb
then the probability of the needle crossing a line is

I am writing a computer program to compute the smallest Primitive
Root g of a positive integer n, g = spr(n). See
http://mathworld.wolfram.com/PrimitiveRoot.html .
In testing the program I have noticed that for p an odd prime

I've posed these problems before separately, but nobody has
been able to solve it so, I'll try again in one message.
Problem 1.
Let N be the integer numbers 1 through K, and let

Some time ago we investigated the problem of sampling, without replacement,
from an urn containing W white balls and T total balls.  The question was
posed for taking two samples.  The object was to have a probability of a/b
of drawing two white balls; a and b being specified ...

I would be interested to know a method, of obtaining integer
solutions to
a^3 + b^3 = 22*c^3
This is not homework; I came across the problem in a popular

1.whats the relationship between the parallelogram and the rectangle?
2. whats the relationship  between the parallelogram and the triangle?
3. what is the relationship between the rectangle and the triangle?

I took a calculus course about 12 years ago, and I don't remember much
of it.  Now I'm taking an artificial intelligence course and my prof
made the remark that most mathematical computation doesn't require AI,
but solving something like

Give me information pls....

Hi!  I am the Jr Mathcounts coach again who occasionally needs help.  Could
anyone give me a simple way to do this that my 6th through 8th graders will
understand (and me too!)?  This is a state level test (very hard for our
team), and I have never done one of these before.  ...

How can you divide a octagon into equal parts with 5 straight lines??

.     Gravity As Thermodynamics:
  The Explanation For The Universe.
There is a fear among thinkers too clever for their
own good that perhaps none of them may prove to be