The Missing Square puzzle, a.k.a. Vanishing Area puzzles are timeless examples of lateral thinking challenges.

To create your own puzzle, follow these steps:

• Download and print the following files on A4 printer paper.

Note: To make the puzzle sturdier, glue a thick paper or a cardboard on the back of the ‘puzzle pieces’ document.

Puzzle 1

• Cut out the square puzzle from the puzzle pieces document.
• Embellish each quadrant with a unique design.
• Place a dot on each piece towards the center of the square.
• Cut along the red lines to produce four quadrilateral pieces.
• Your puzzle is now complete.

Here’s how it works:

• Position all four pieces on the ‘Missing Square Puzzle Grid’ to form a 4×4 square. That makes a perfect square as shown below:

• Now, rearrange the pieces like below. Rotate each one by 180 degrees so that the center corner of each piece aligns with the corners of the main square.

• Although the four pieces still created the same square, you will notice a “missing square” in the middle! Can you figure out what’s going on?

Puzzle 2

Amazed? How about exploring a similar concept with a triangular puzzle. Do you think you can rearrange the below puzzle without a missing square?

• Cut the right-angle triangle pieces from the ‘Puzzle Pieces’ document.
• Arrange all four pieces to make a right-angle triangle. So perfect!

• Let’s try to rearrange the pieces as illustrated below.

• Both right angle triangles look the same size. But wait, once again we have a “missing square”!

What is going on?

In the first puzzle, when you rearrange the pieces, they slightly overlap the edges of the square. While we think it perfectly fits in the square grid, this slight overlap makes all the difference. It creates enough area for one square😊.

Similarly in the second puzzle, when you rearrange the pieces, there will be a slight overlap on the edges of the triangle puzzle. This is just enough to create the missing square.

Such hands-on puzzles are not merely entertaining; they provide a concrete way to understand fundamental yet significant mathematical concepts. Remember, true comprehension starts with practical experience. Hope you enjoyed some math and magic! Try practicing it yourself and amaze your friends!