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Math Fair Category: 3D Objects & 2D Shapes

An Amoeba’s Meaning of Life

In this puzzle, we explore the world of 2-dimensional geometry by constructing and analyzing shapes, such as pentagons, triangles, and squares. It introduces us to…

Babushka Squares

In this investigation, we work with pentominoes, five squares, and triominoes, 3 squares, where we study the unique shapes from constructing them in all different…

Training Trains

When in grade 1, locomotives learn by going round and round in circles on specially created tracks like the one on the right. The circular…

Un-Babushka Squares

When, Polyo, wants to rebel from her claustrophobic family, she seeks out solitude to work on very Un-Babushka-like puzzles. That means she wants puzzles where…

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…

Vermeer’s Paintbrush

When painting this painting of a music lesson, Vermeer, the great Dutch artist, dropped his paintbrush on the tiled floor. He noticed that two ends…

Twinkle Twinkle

Carl Sagan and Joseph Campbell were walking on the Milky Way last evening. Carl turned to Joseph and said “What a lot of stars!” “But…

Touching Circles

Fill the following triangle with red, yellow and blue circles so that no circles of the same color are next to each other. Extensions: Is…

Tiling on Titan

The Wise Women of Titan want to re-tile the enormous rooms of their palace using rectangles, but for aesthetic reasons they do not want identically…