Working systematically

Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

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

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla 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 Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios 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?