Working systematically

How many trapeziums, of various sizes, are hidden in this picture?

Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

A 1x2x3 block is placed on an 8x8 board and rolled several times.... How many squares has it occupied altogether?

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

Weekly Problem 11 - 2011
Kanga hops ten times in one of four directions. At how many different points can he end up?

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?