Created by Martin Gardner in 1961
The Vanishing Area Paradox Created by Martin Gardner

Can you explain this ? This is a real classic among the riddles that circulate the internet.

Click here to show an explanation. The outside border of the elements is curved a little bit. In the first picture they curve inwards. In the second they curve outwards, just enough to make the hole.

Comments

Leave a Comment
246 - Thursday 4 August 2011

i think the eplaination i wrong;the blue and red triangle switched positions, causing the hole.

Chris - Saturday 20 August 2011

The red and blue switch places, but the orange slides down onto the green and, due to the number of blocks, makes a hole. What is so hard or impossible about this??? It seems rather simple to me.

Akiva - Wednesday 28 September 2011

The impossible is that, even though they are made of the same pieces, they have different areas. This is just like, after learning a toddler has cut out a square of your carpet, you can just cut up the carpet, rearrange the pieces, and have it end up with the same area as before.

CM - Tuesday 15 November 2011

Chris, the hard part is this: we have 4 geometric figures with a given area, no matter what is the position they have, the area is allways the same, so if we rearange the figures, no matter what is the design, the area occupied must be the same. Now, count the color squares in first figure, next count the ones in the second, note there is a white square in the second (yes i know white is a color). if the draw is correct something is wrong with both pictures, areas are different, thats the riddle