## Math Puzzles Geometry, Spatial Reasoning and Visualization

• #### Around the World

The circumference of the Earth is 40,076 km (24,902 mi). Let’s say we had a rope that long and used it to circle the Earth, like the red line in the picture.

• #### Boxes, Cubes, and Nets

We have puzzles on polyominoes, but here's one on how to make pentominoes and hexominoes with an extra dimension.

• #### Build a Cube

How many ways six squares be arranged to form a cube? Come give it a try, then see what we came up with!

• #### Can You Build A Wall around France?

The Great Pyramids at Giza in Egypt were built nearly 5,000 years ago as tombs for the Pharaohs.

• #### Connected Loops

This puzzle challenges you to find a way to tie the three loops of string together so that untying any one of them causes the other two to be disconnected.

• #### Four Square Matchsticks

Using four matchsticks of equal length, we can enclose an area of one square matchstick.

• #### How Can This Be True?

This month’s math puzzle was submitted by Dougal McVicar.

• #### How Can This Field Be Evenly Divided?

An old farmer in Seedonia was getting ready to retire.  He wanted to pass his farm on to his children with half going to his son and the other half to his daughter.

• #### How Fast Are You Moving?

Right this minute. Sitting or standing in front of your computer monitor—or reading this on a printed sheet of paper—how fast are you moving?

• #### How Long Is the Coast of England?

…asked mathematician Benoit Mandelbrot. This math puzzle explores questions related to fractal geometry.

• #### How Many Regular Mosaics Can You Make?

This regular mosaic is a pattern made up of equilateral triangles.

• #### Is It Straight?

Mitchell hung a mirror on the wall in his house. To make sure it was perfectly straight he measured exactly 40 cm (16 in) from . . .

• #### Land and Water

An elderly farmer in Seedonia decided to pass his farm on to his four children by dividing the land up equally among them.

• #### Trees in a Row

You have seven trees to plant. They need to be arranged in six rows with three trees in each row. How do you do it?

• #### More Trees in a Row

You have ten trees. Can you arrange them in four rows of five?

• #### Nets for Polyhedra

In the Boxes, Cubes, and Nets puzzle we found nets—two-dimensional shapes that can be folded up to form a three-dimensional shape—to fit cubes. This puzzle we try to find nets to fit polyhedra.

• #### Painted Cube Face Patterns

Start with a set of wooden building blocks in the shape of cubes.

• #### Rearrange the Coins

Rearrange six coins from a triangle to a circle in the fewest possible moves.

• #### Tennis Ball Container

You have a cylindrical container just big enough to hold three tennis balls.

• #### Toothpick Puzzles

Toothpick puzzles (more commonly called “matchstick puzzles”—but it’s safer to use toothpicks than matchsticks) are an old form of geometric puzzle.

• #### Toothpick Triangles

Toothpick puzzles can be done with many different geometric shapes. Here, we use triangles for our puzzles.

• #### Where Are You?

If you are standing somewhere on the Earth, can you to figure out where in the world you must be based on the information we give you?

• #### Which Letter Is This?

This puzzle is attributed to Scott Kim.  He cut out an uppercase letter from a piece of paper and then made one fold.