Geometry - Brain Easer

Difficulty - Medium, Geometry, Paradox

Coin Rotation Paradox

The coin rotation paradox is a famous math problem with an unintuitive solution:

If you roll a coin around the edge of another coin of the same size, from an external perspective, how many rotations does the coin make by the time it returns to its original position?

Difficulty - Medium, Geometry

Area of the Rectangle

The shaded rectangle is tangent to the circle at the two points indicated, and its bottom right corner lies on the circumference of that circle. What is the area of the rectangle?

Difficulty - Easy, Geometry

Maximize Triangle Area

If a triangle has two sides with lengths 3 and 4, what should the length of the third side be in order to maximize the area of the triangle?

Difficulty - Hard, Geometry

Four Lines of Four Coins

Form four lines of four coins by moving exactly 3 of the coins below:

Rules:

Coins cannot be stacked on top of one another.
A line of five or more coins is still only considered one line.
The centers of the coins must be precisely on the same straight line, but can be anywhere on the line.
Lines can be any length, and can be horizontal, vertical, or diagonal.

Difficulty - Medium, Geometry

Inscribed Squares

Above are two identical isosceles right triangles containing two inscribed squares.

In one, a perfect square has been inscribed such that two sides line up with the two legs of the right triangle. In the other, a perfect square has been inscribed such that one side lines up with the hypotenuse of the right triangle.

Is the inscribed square on the left larger or the one on the right?

Difficulty - Very Easy, Geometry

Measuring Sticks Puzzle

What is the length of the longest stick?

Difficulty - Hard, Geometry, Matchstick Puzzles

Make Five into Four

Move exactly 3 matches to make these five squares into four squares of equal size, without any matches left over.

Difficulty - Medium, Geometry

Blue and Red Maze

In this maze, you must alternate going through blue and red doors – in other words, you cannot go through two blue doors in a row or two red doors in a row.

Entering through the blue door in the top left, can you find your way through the maze and exit through the red door in the top right?

Difficulty - Hard, Geometry, Matchstick Puzzles

Four Squares Match Puzzle

Move exactly 2 matches to make these five squares into four squares of equal size, without any matches left over.

Difficulty - Hard, Geometry, Matchstick Puzzles

Four Triangles with Matches

Move exactly 3 matches to make these three equilateral triangles into four equilateral triangles of any size, without any matches crossing or overlapping.