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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…

The Greener Lily Pad

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…