Puzzles involving any geometry, including shapes, areas, distances, and angles
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?
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?
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?
Form four lines of four coins by moving exactly 3 of the coins below:
Rules:
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?
Move exactly 3 matches to make these five squares into four squares of equal size, without any matches left over.
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?
Move exactly 2 matches to make these five squares into four squares of equal size, without any matches left over.
Move exactly 3 matches to make these three equilateral triangles into four equilateral triangles of any size, without any matches crossing or overlapping.
