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Maximum Area Given Enclosing Lengths [11/21/2001]

I am given the lengths of a set of N line segments and I am supposed to calculate the maximum area that can be enclosed using them. Is there an efficient method of finding the solution?

Monte Carlo Approximation of Pi [11/24/2001]

Using the circle-in-square model, find an algorithm to determine the value of pi.

Multiple Linear Regression [01/23/1997]

What are the formulas needed for multiple linear regression?

Multiplying Sparse Matrices [12/01/2000]

Is there a reasonably fast way to multiply two matrices that are very big, but sparse (they have many zeros)?

The Official Euclidean Algorithm [11/16/2000]

Can you state briefly the "official" Euclidean Algorithm?

Polynomial Congruence [02/28/2001]

Find a polynomial (F) in Field(7) with degree less then 4...

Positive Unit Fractions [10/02/2002]

Find five different positive unit fractions whose sum is 1. (A unit fraction is a fraction whose numerator is 1. All denominators must also be natural numbers.)

Power Spectrum [01/29/1998]

I'm currently writing a program that will show the power spectrum of a sound using a microphone as an input... When I do a FFT I get a complex number and just take the magnitude. Is there a more efficient way of doing this?

Producing MOD(x,y) with Arithmetic Operations [03/04/1998]

Is there any way to produce the "MOD(dividend,divisor)" spreadsheet function using basic arithmetic operations?

Programs to Find Prime Numbers [11/27/1996]

Can a program be written in BASIC to compute the number of prime numbers smaller than n?

The Risch Algorithm [11/30/1998]

Is there a known algorithm for simplifying and integrating mathematical functions of one variable? What is the Risch algorithm?

The Simplex Method [11/2/1996]

How does the simplex method work and what would I use it for?

Solutions for Pell's Equation [12/11/2000]

Do you know of an algorithm to find solutions for Pell's equation (x^2 - Dy^2 = 1) for different values of D?

Solving Nonlinear Systems with Many Variables [10/25/2000]

Do you know a numeric algorithm that solves systems of non-linear polynomial equations with up to 10 variables?

Square Roots Without a Calculator [8/6/1996]

How do you get a square root without a calculator? What is the square root of 7 to 5 decimal places?

Strategy for Playing Mastermind and Similar Games [03/26/2007]

I'm trying to guess a 4-digit number with unique digits and after each guess I'm told how many digits are correct and in the right place and how many are correct but in the wrong place. I use that feedback to make better and better guesses until I find the correct number. Is there a general strategy to minimize the guesses needed?

Sum of Reciprocals [08/05/2008]

Find seven unique positive integers such that the sum of their reciprocals is 1.

Z Transforms and the Fibonacci Sequence [04/20/1998]

Can you suggest an example of using Z transforms to derive the equation of a Fibonacci number?

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