## The Inevitable Knot in Your Long Extension Cord

This knot in my extension cord occurred inadvertently and thus I assumed with the highest likelihood it could be undone with a single pass through a cable end through a loop or loops with the loops arranged so only a single pass is required.  You would think this because once the Read more…

## 536 Puzzles: #309: A Maypole Puzzle

During a gale a maypole was broken in such a manner that it struck the level ground at a distance of twenty feet from the base of the pole, where it entered the earth. It was repaired, and broken by the wind a second time at a point five feet Read more…

## Solve System of Equations X+YZ=6 Y+XZ=6 Z+XY=6

Research LInks Brain Teasers and Puzzles Find the solution for the system of equations:                               Multiply each equation by the term missing to make each second term a triple               Read more…

## Euclidean Algorithm for Greatest Common Denominator

Research Links Wikipedia: Euclidean algorithm A 24-by-60 rectangle is covered with ten 12-by-12 square tiles, where 12 is the GCD of 24 and 60. More generally, an a-by-b rectangle can be covered with square tiles of side-length c only if c is a common divisor of a and b. So the task is to find the largest square that tiles Read more…

###### Math

A farmer has 100 dollars to buy 100 animals.  A cow costs 10, a pig costs 5 and a chicken costs 50 cents.  How many of each does he buy?  He must use all his money and he must buy at least 1 of each type. note Z must be even Read more…

## Polynomial Root Solver with Root Map in Complex Plane and Graph of Function

Research Links Root Finder Wolfram Widget Gallery

## Eulers Theorem

Research Links Wikipedia: Eulers Theorem Wikipedia Euler Totient Function Online totient calculator Euler's theorem derivation   Eulers theorem is very similar to Fermat's little theorem.  It is not restricted to prime number p.  It is restricted to relatively prime a & p.  It states:   Where  is the Euler totient Read more…