# 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…