Working systematically

How many possible symmetrical necklaces can you find? How do you know you've found them all?

Lola bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lola have paid for the balloon?

On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?

On the planet Vuv there are two sorts of creatures. The Zias have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zias and how many Zepts were there?

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the shapes?

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

Amy's mum gave her £2.50 to spend. She bought four times as many pens as pencils and was given 40p change. How many of each did she buy?

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

Can you replace the letters with numbers? Is there only one solution in each case?