Sunday Times Teaser 2556 – Dotty Squares
by Andrew Skidmore
Published: 18 September 2011 (link)
On a piece of paper I have drawn a neat, evenly spaced square array of 36 dots, namely six rows of six.
If I were to ask you how many squares are formed, you might say just 25, for the array seems to consist of 25 little squares. However, lots of sets of four of the dots form the vertices of a square.
How many ways are there of choosing four of the dots so that they form the vertices of a square?