We know that this is difficult to believe. Even enlarging the image and examining it closely fails to convince you. For instance in the image on the left would you believe that the knight on the top is standing on a square that has exactly the same grey value as the square on which the lower knight is standing? Even if you stare at the picture for a long time and concentrate intensely your eyes and brain will tell you that the bottom one is clearly lighter. One way to convince yourself is to punch two small holes in a paper and hold it up to the screen, so that only the knight and the squares on which they stand are visible. You will see that the are exactly the same. We have done this electronically in the following image:

Another way is to copy the image into a paint program and use the colour pipette to determine the colours. Even better: cut out a small section of knight and square and insert it as a floating element in the picture. Move the section to its original place and then to the over to the same location on the other knight. You will see that it blends in perfectly.

Here's a small animation that shows the knights changing places.

Can you believe that the squares marked A and B in the above picture have exactly the same? If you use a pipette to examine the squares you will see that both are exactly the same shade of grey (RGB = 107, 107, 107) Once again closer scrutiny does not help. Or are you able to convince yourself that an identical shade of grey was used in the picture on the right?

We can try the experiment in the real world. Here's a picture of a chessboard with a shadow cast over the left side.

Which square is lighter, A or B? The answer is B! If you cut out a bit of the B-square and move it over A you will see that it is actually slightly lighter than A.

In greyscale the effect remains unchanged: the cut-out in the picture above was taken from B and inserted in A. It is clearly lighter than the surrounding.

A description of the illusion is given at Prof. Adelson's web site. Essentially it says that our visual system does not simply measure the light coming from a surface, but interprets the luminance in the context of its surroundings. The brain knows that a light surface in a shadow may reflect less light than a dark surface in full light. Adelson explains how the brain determines where the shadows are and how to compensate for them in order to determine the shade of gray that belongs to the surface.

"The first trick is based on local contrast. In shadow or not, a check that is lighter than its neighboring checks is probably lighter than average, and vice versa. In the figure, the light check in shadow is surrounded by darker checks. Thus, even though the check is physically dark, it is light when compared to its neighbors. The dark checks outside the shadow, conversely, are surrounded by lighter checks, so they look dark by comparison.

A second trick is based on the fact that shadows often have soft edges, while paint boundaries (like the checks) often have sharp edges. The visual system tends to ignore gradual changes in light level, so that it can determine the color of the surfaces without being misled by shadows."

It is important to note that none of the above is a defect in our visual system, but rather a very sophisticated system that process the data that it receives. "The visual system is not very good at being a physical light meter, but that is not its purpose. The important task is to break the image information down into meaningful components, and thereby perceive the nature of the objects in view."

The correct solution

So unfortunately we will have to modify the solution we gave above. Both knights might be exactly the same shade of gray, as are the squares on which they stand. But the human eye and brain process the image correctly and tell us that the one in the middle is a white knight on a white square and the one on the top a black knight on a black square.

Putting it another way: if you set up a real chess board with the objects positioned as above, using a white and black knight, then you will get exactly the same result as in the above picture. Just because on the photographic plate the two pieces and squares have the same shade of grey does not change the white knight into a black one, or the white square into a black one. We simply have to accept that our cognitive system understands shadows correctly and still recognises that the knight in the middle is white.

You can also write to us if you need to communicate any further thoughts with regard to this incredible puzzle.

Frederic Friedel

In closing here is another little image you might find a bit irritating. Or can you see that there is no "bulge" in this picture, but that all lines and squares are perfectly straight.

There are more interesting examples on Akiyoshi's illusion pages.

A selection of responses received so far

Dubravko Mazur
My daugter bought me one of those crystal glass chess set. It looked neat for the room decoration and all was fine untill I tried to play chess on it. To start I automatically assumed that clear squers and pieces are white and sanded ones black. However, the table I set it on has black frame with transparent glass top. Shortly after starting to make moves my "chess brain" became quite confused. What to tell you?! I'm avoiding to use that set for chess playing!?!

Professor Christopher Willard, Montreal, Canada
There is no white knight, they are both the same middle grey. And in fact, the squares both knights sit on are also the same middle grey as the knights. It's easy to guess this was your goal, and it is easy to prove by punching holes in a white paper and comparing the greys.

The diagram provides a striking example of what was called "simultaneous contrast" by Josef Albers and what today is known as 'chromatic induction." I must congratulate you on this terrific example. You may also be aware the Germany has a longstanding history of important color theorists including Goethe, Itten, and Albers, to name but three.

When a middle grey paper is placed on a lighter background it appears darker and when the middle grey is placed on a darker background it appears lighter. This is due to inhibition and exitation functions at a retinal level (although I won't bore you with the details here.) In this case, as I'm sure you know, the darker areas of the board where the shadow is cast make the grey of the bottom knight appear lighter, and the lightness of the background and lighter squares make the top knight appear darker. By the way it works in a similar way for color.

As a professor of color theory who teaches this stuff on a daily basis, I have but one question for you: how in the hell did you get involved with this idea? I can't believe chess enthusiasts dabble as frequently in the subtle effects of combinations of greys as we artists do in the world of chess. You've certainly done better with chromatic induction than I do with my openings!

Chris Taylor
Light as to do with visual, or as a weight? Hmm, I don't think this is crazy, just bizzare!

Mendi Barel
U crazy. It very simple that the upper is the black. Why u spend time? What was the problem?

Kevin Breen
I love this puzzle. I believe the correct answer to the the question of which is the white knight is it can't be determined. Both knights are the same exact color.

Kirk S Johnson
Heres my reasoning of the puzzle :) Assuming the pieces are opaque, the two knights have the same brightness intensity in the image. However, The Knight in the middle is in the shadow of the Cylinder. Therefore is the lighter Knight (white). Similarly, the square in the middle and that on top have the same "intensity at the pixel level", however, due the shadow cast on the middle square, it should be the white square (lighter).

Andrew Goldberg
Being somewhat knowledgable about photography my guess is that, even though your wording is awkward and ambiguous, your looking for the knight that has the most "light" on it, which is the darker colored one, since its in the light waves of artificial or sun-made light particles, and the white knight - that is the lighter colored of the two - is in the shadows and therefore has the least light on it, hence is the darkest.

Riyad Twair
I photoshopped your puzzle and I couldn’t believe my eyes. Impressive, I still can’t believe it. Probably the best optical illusion I’ve ever seen. NICE!

Jari Harjula
Nice one. Had to use the GIMP to figure it out. After seeing that they are all of color #6b6b6b (the same shade of gray) you just have to ignore what your eyes are telling you...

Cyrille Viossat
They are exactly the same. No difference in colour at all. However, the white knight is the one in the shadow. If you put your chess set in a dark room, I expect you can still call half of the men white.

Dr. Miguel Zialcita
Insane and probably a waste of time but intriguing, nonetheless! So is it a play on words? After all "lighter" may refer to weight or, perhaps, the relative illumination of the item in question, as well as the color and hue. I will await your solution.

Alan Gardiner
Interesting optical illusion. Due to the shadow cast by the cylinder, both knights and both squares in question are all the same intensity, or shade of grey. Thanks for publishing this. Keep the puzzles and tactical problems coming!!

Luis Enrique Rodriguez
1) Los caballos no están sobre el tablero, esta un poco más arriba del mismo. 2) El caballo que aparece más oscuro, realmente es el más claro, pero se ve oscuro porque esta a la sombra del cilindro. Es decir, la luz no le llega. 3) el caballo mas claro, es el más oscuro, ya que, aunque le de luz, no queda totalmente blanco. Este caballo, como no esta a la sombra del cilindro, debería proyectar sombra, pero parece que por la altura que tiene sobre el tablero, la sombra cae fuera de este. La solución me vino de buscar sombra en el caballo que esta arriba a la izquierda, pero no tiene, entonces debe estar detrás del cilindro.

John Brondum
Wow they are the same color! I used Corel Photo Paint to cut them out and place them over one another. I'm into photography and graphics enough to suspect that the environment might be skewing our perspective, but even knowing that it was still hard to believe. Very interesting thanks.

Elliot Cuzzillo
The two squares are exactly the same color, as are the two knights. The only thing different is their surroundings. Since the square in the middle is surrounded by much darker squares, and (since we are chessplayers) we identify these much darker squares with the square the top knight is sitting on, (and the top knight is surrounded by much lighter squares) we think of the top knight and square as dark, and the central knight and square as light. In fact, if one looks at them without their surroundings (I put a tissue on my monitor to block out the immediate surroundings), they are either identical in intensity or they are too close for the human eye to discern the difference. Thanks very much for posting the puzzle.

Papamix
The white knight is obviously in the middle of the board and I'm not gonna fall into such stupid tricks. The cylinder is going to make you think about the shadow it casts over the middle knight square but this is something more to make you think meaningless and lose your time. Hey, will someone prove me that I'm blind and I don't understand the difference of white and black?

Lee Pierson
Can you tell us something about the colors of the sources of illumination on the chessboard?

Mahmud Chowdhury
Both knights of the same colour, and the same is the case with the actual colour of squares the knights stand on (though of course in even lighting the center square is lighter coloured). Our eyes seem to be fooled into believing the colours are different because they use the surrounding shades of gray and the location of blurred shadow boundaries to assess the colours of the knights. If only there was a way to make our opponents mistake the colours of the pieces in a game.

Joachim Heuser
Since both the squares and the pieces have the same color (both knights are black - quite nice to see if you punch holes in a sheet of paper and hold it over your screeen), you'll have to wonder if this could be helpful in a blitz game with two knights down. Just place your Coke on the edge of the board and offer your stunned opponent a draw since his advantage seems to have vanished. Just be sure to reset the starting position *really* fast and leave the playing room.

Mathieu Cloutier
You are just a bunch of photoshop geeks :) The CMYK spec of the two knight's colors are exactly the same. You had me for a moment! Keep up the good work!

Paul V. Allen
Totally trivial visual illusion. Cut two small holes in a piece of paper at distance equal to distance between centers of knights. Then explore knights and square around them, and they are obviously identical. Explanation equally trivial. Brain's visual experience says an object of given apparent brightness in shade is more intrinsically bright than an object of the same apparent brightness that is not shaded. So that is what your brain insists on seeing.

Michalis Kaloumenos
Congratulations guys, you got the absolute illusion. Both knights have exactly the same color. This can be verified by any "eyedropper tool" of a photoshop-like program. So, we have a chessboard. Dark and light squares. It is quite embarrassing to find out that the light square (upon which a knight stands) has the same color as the dark square upon which stands the other knight. Yet, the eye calls the one square "light", the other "dark". Because this is the only way that the eye can adopt the chessboard pattern. It is easy for the eye to assign the same color of the square to the knight that stands upon. This mechanism of nature I admire and I have not an answer for. Many thanks for the beautiful work.

David Campbell
I think the answer to both questions is "neither". The shadow effect on the squares and knight in the middle of the board optically confuses the brain into being tricked (due to comparing neghbouring shades). As the "dark" square at the edge of the board has pure white (at the edge of the board) to be compared to, logic states that the square must be dark. Upon closer inspection, I would say that both knights and squares are the same colour!

David Slauenwhite
Truly a bizarro puzzle of bizarre puzzels.

David Rabel, Institut de Biologie Moleculaire et cellulaire
These two knights are strictly identical! but one of them are in the shadow of the big cylinder, so it's lighter than the other in the "reality" (the white one), but in this picture they are exactly the same in terms of color (CMYK). Very interesting picture....

William Hoggarth
The colour of both knights and both squares is the same! The illusion that the colours are different is created by utilising the fact that the brain makes use of contrasts when making sense of an image. An excellent example of this phenomen! I've always known my chess vision was a bit dodgy ;-)

David Lundstrom
They are the same colour - is my theory! Thanks for the great site..