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Compare the Squares

Stage: 2 Challenge Level: Challenge Level:1

This was a tricky problem! Isabella from Sion Manning RC School for Girls said:

I think the squares are different colours, because the order in which squares appear on the board are - black, white, black, white etc. On either side of square B are two black squares therefore B must be a lighter square - whereas A is a darker square.

She then asked ten people whether they thought the squares were the same colour or not. Here is a table of her results:



Person Same Different
A x
B x
C x
D x
E x
F x
G x
H x
I x
J x

She goes on to say:

80% of people think different colours.
20% of people think the squares are the same colours.
I still think square A and B are different colours.

Then she showed the same people the second picture. Here is the table of her results this time:


Person Same Different
A x
B x
C x
D x
E x
F x
G x
H x
I x
J x

1 person changed their mind - 30% of people think the squares are the same colour.


Did this second survey change Isabella's mind? She wrote:


No, because it is still clear that square B, is supposed to be white.
However after pasting the picture into "Paint" and colour sampling it, I discovered that the squares are the same colour (so says the computer software). Also the colour of the actual letters "A" and "B" change in both sets of data, which perhaps causes your eyes to think they're the same colour.

That's an interesting observation about the colour of the letters, Isabella, and I agree with you, it might well help to "trick" your eyes.

Rohaan from Longbay Primary School explained further:


On chessboard no.1 square B is white not grey. if you take the cylinder away there would be no shadow so square B would not look grey. On chessboard no.2 if you compare the strips with square A they are the same colour. If you compare the strips with square B they're the same colour, so it makes sense that square A and square B are the same colour.

Well done to all of you.