# Math Fair Category: Variables & Equations

## Barbanegra the Pirate

The crafty British pirate, Blackbeard (Spaniards called him Barbanegra), had a keen mind for mathematics. The following are excerpts from a diary found in a…

## XYZ Tree

Find 3 positive integers x, y and z which satisfy this equation: Using this solution, find a different solution by changing one and only one…

## Walls of Rock

Beaumaris castle in Wales was the largest of the Welsh castles built by King Edward I (r. 1272-1307) Construction began in 1295, but was never…

Frogs have a saying: “The Other Lily Pad Is Always Greener”. Some green and yellow frogs were arguing about this until they agreed that they…

## Tetrahedrons Snuggling

On a cold winter evening, Olive, the green tetrahedron said to her identical quadruplet sisters “It’s so cold that my vertices are numb, my edges…

## Sword of Knowledge

The Dragon of Ignorance has three heads and three tails. You can slay it with the Sword of Knowledge, by chopping off all its heads…

## Snow Day Phone Chain

On Thursday January 20th the Pocono Mountain region experienced the first big snow storm of the new millennium. Many schools closed because of the slippery…

## Snazzy Triangle

There is a number 6 on the tip of the triangle. Arrange the numbers 1, 2, 3, 4 and 5 such that the sum of…

## Rocket-Propelled Coyote

Coyotes demarcate their territory by peeing on bushes, rocks, shrubs, cacti, trees, and anything else that is lying around. It is tiring, never-ending work. That…

## Ring of Threes

Write 1’s and 2’s in the circles so that no three consecutive numbers sum to a multiple of three. Extensions: There are four solutions to…