Math Forum / Mathematics / Recreational Math / August 2007

I have recently been playing with some problems in Hamming's, The Art
of Probability.  I'm having difficulty understanding two of the solved
problems and would appreciate any walkthrough to the solution.
Question 1: on page 47 question 2.2-14 reads: "Using all the letters

GOOD EVENING!
Puzzle 192 is about odd sized pizzas. Once again a geometry problem, but a
lot simpler than last weeks puzzle. Nevertheless I hope it is to your
liking. Don't hesitate to send me your solution.

Having come off a tremendous research effort that has given key
answers to important questions with surrogate factoring, I find myself
still curious about the math world's ability to ignore a factoring
idea that has many indications that it should be possible to get it to

I would like to implement logarithmic fading instead of linear in my
sound code but I do not know how to go about it. Here is the linear
solution, can anyone please suggest a logarithmic replacement? thanks
m_currentGain = m_beginGain + ( ( elapsedFadeTime / m_fadeDuration ) * (

I finally am getting a handle on a crucial metric for determining how
likely you are to factor using what I call surrogate factoring where
if your target composite to factor is T, the following equations
x^2 = y^2 mod T

After my failure with what I deluded myself into thinking (for a
while) was the perfect factoring algorithm, I just bit the bullet and
began the detailed and tedious analysis that my latest insight
indicated which took me into the calculus which was kind of fun, and a

Yesterday I started with a long and detailed post talking about the
latest insight with my factoring research, but after that post I had
several more claiming that I had now solved the factoring problem
which all were flawed.

Wow, I didn't know the solution to the factoring problem would turn
out to be that simple.
It seems strange to think back over the years since I first started
looking at factoring one number by using another and consider all the

Algorithm for guaranteeing the factorization of a target composite T
of any size.
Use (x+k)^2  = y^2 + 2k^2 + n*T.
1.  Pick k=2 and an n that gives you an absolute value of 2k^2 + n*T

While changing channels today I heard a preacher talk about
the significance of the number 153 in the Bible chapter John 21
(I changed channels before he got around to explaining it).
A Google search on "153 "John 21"" produces, among other sites:

I am trying to calculate Pg, the odds that Player A will win a game in
tennis against Player B, given Pp = probability that A will win any
single point (on average). I am treating all points as equal for the
moment.

ON August 9th I stepped through integer factorization equations in my
post "JSH: On integer factorization" and earlier today I thought some
more about when that approach might work to give a non-trivial
factorization.

After the explanation of my current factoring research that I just
posted I realized that wrapped up in this latest analysis is solution
to the factoring problem.
It's fairly easy but as usual I'll post what I think it is to see if I

Can someone please solve this for me I need whole procedure not just
the final solution:
a, b and c are vectors. c is linear dependent on a+b. In other words c
= x (a+b) where x is real number.

Here's a post to go over the latest with my factoring research and
explain a key breakthrough, as well as address the issue of
demonstration.
First some background, since August of last year I have focused on