Square deal

The diagram shows 4 by 4 dots How many different squares can you draw so that the four corners of each square lie on the dots?

What about 5 by 5 dots?

Age 13-15

A matter of minutes

At 2 o’clock the angle between the hands of a clock is 60 degrees.

What is the exact time between 2 and 3 o’clock when the hands are at right angles?

SOLUTIONS

Square deal

A total of 20 squares can be drawn on a 4 by 4 array of dots, 14 with sides parallel to the edges of the array and 6 ‘on the skew’. On a 5 by 5 array, 50 can be drawn, 30 with sides parallel to the edges of the array and 20 ‘on the skew’.

A matter of minutes

The hands of the clock are at right angles at 273Z11 minutes past 2. When they are at right angles the hands are at 15 minutes apart. Let m equal the number of minutes that the minute hand has moved since 2 o’clock. In the same time the hour hand has moved mZ12 minutes from the 2 o’clock position.

So: m - 15 = mZ12 +10, giving m = 273Z11