Working systematically

In how many ways can you give change for a ten pence piece?

What is the smallest number of ferry trips that Neda needs to take to visit all four islands and return to the mainland?

Can you remove the least number of points from this diagram, so no three of the remaining points are in a straight line?

The squares of this grid contain one of the letters P, Q, R and S. Can you complete this square so that touching squares do not contain the same letter? How many possibilities are there?

This grocer wants to arrange his fruit in a particular order, can you help him?

Weekly Problem 21 - 2011
How many ways can you paint this wall with four different colours?

In a 7-digit numerical code, each group of four consecutive digits adds to 16, and each group of five consecutive digits adds to 19. What is the sum of all 7 digits?

Can you work out the sum of the missing digits in this subtraction?

I made a list of every number that is the units digit of at least one prime number. How many digits appear in the list?

Weekly Problem 31 - 2016
The diagram shows a grid of $16$ identical equilateral triangles. How many rhombuses are there made up of two adjacent small triangles?