Working systematically

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?

You have 5 darts and your target score is 44. How many different ways could you score 44?

Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?

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?