Checkerboard problem

I know the answer to this conundrum, but I still have problems recognizing the answer. If you’ve never seen it before, it is really baffling.

Which is the true statement about the image below?

  1. Square A is a darker grey than square B.
  2. A and B are the same shade of grey.
  3. A is lighter than B.

Adelson's checkerboard problem

(Click to enlarge to full size. It might help.)

The illusion was invented by Edward H Adelson in 1995. The best way to work out the solution empirically rather than by sight is either to import the full image into Photoshop (or whatever tool you use for image processing) and use its eyedropper tool to find the RGB values, or to print it out and then cut out the two squares to compare them directly.

If you want to explore this illusion more, I would go to the source: Adelson’s pages about it.

Now playing:
Thievery Corporation - All That We Perceive
(from It Takes A Thief)

Loading similar posts...   Loading links to posts on similar topics...

5 Responses

#1 Malcolm Groves said...
08-May-12 7:43 PM

That's very cool. I read the proof and the explanation, and while I believe it, I still can't see it in the original image.

Apart from the reasons given in the proof (which make sense) I guess it's also because we "know" what a checkerboard should look like, and so the column and row positions of the two squares reinforce that they should be different colours. I wonder would the illusion be as strong if it was on a board with an unfamiliar pattern?

julian m bucknall avatar
#2 julian m bucknall said...
08-May-12 8:34 PM

Malcolm: I can't see it either. I'm placing pieces of paper on the screen to block stuff off, etc, etc, but it remains maddeningly obvious that A is darker than B...

Interesting thought about a different pattern: I'd have to say that the problem would be in making a convincing fake shadow.

Cheers, Julian

#3 Mike Jackson said...
10-May-12 1:12 AM

In addition to Addison's two explanations, I think I see a third. Using the eyedropper tool on the 'A' & 'B' characters themselves, the 'B' character is somewhat darker than the 'A', increasing the contrast with it's surrounding square. But I still can't 'see' the trick either!

#4 David said...
18-May-12 2:33 AM

I placed a pen to cover all of the squares between square a and b and the colours appeared the same. Mind I had to block every part of the shadow. Leave any part of it there and the illusion remains.

#5 David said...
18-May-12 2:35 AM

Damn - tried it again and they look different

Leave a response

Note: some MarkDown is allowed, but HTML is not. Expand to show what's available.

  •  Emphasize with italics: surround word with underscores _emphasis_
  •  Emphasize strongly: surround word with double-asterisks **strong**
  •  Link: surround text with square brackets, url with parentheses [text](url)
  •  Inline code: surround text with backticks `IEnumerable`
  •  Unordered list: start each line with an asterisk, space * an item
  •  Ordered list: start each line with a digit, period, space 1. an item
  •  Insert code block: start each line with four spaces
  •  Insert blockquote: start each line with right-angle-bracket, space > Now is the time...
Preview of response