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Brain Teasers and Puzzles

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?

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Brain Teasers and Puzzles

Four Lines of Four Coins

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

Four Rows of Four Coins

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.
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Brain Teasers and Puzzles

Inscribed Squares

Squares Inscribed in Right Triangles

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?

Categories
Brain Teasers and Puzzles

Measuring Sticks Puzzle

Measuring Sticks Puzzle

What is the length of the longest stick?

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Brain Teasers and Puzzles

Make Five into Four

Four Squares Match Puzzle

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

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Brain Teasers and Puzzles

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?

Blue and Red Maze
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Brain Teasers and Puzzles

Four Squares Match Puzzle

Four Squares Match Puzzle

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

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Brain Teasers and Puzzles

Four Triangles with Matches

Four Triangles with Matches Puzzle

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

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Brain Teasers and Puzzles

Square in a Square

Square

In the larger square, there is a smaller square formed by lines connecting each corner to the midpoint of one of the sides.

Question: What fraction of the larger square is the smaller filled square?

Categories
Brain Teasers and Puzzles

Unclear Perimeter

Unclear Perimeter Diagram

What is the perimeter of the outer rectangle? All angles shown are right angles.

Categories
Brain Teasers and Puzzles

Five’s a Crowd

Try to place five points in (or on the perimeter of) an equilateral triangle with side length 10, as to maximize the distance between the points.

Equilateral triangle

What is the greatest possible distance between the two closest points?