Working systematically

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?

What is the smallest integer where every digit is a 3 or a 4 and it is divisible by both 3 and 4?

Two of the four small triangles are to be painted black. In how many ways can this be done?

In the multiplication table on the right, only some of the numbers have been given. What is the value of A+B+C+D+E?

This task follows on from Build it Up and takes the ideas into three dimensions!

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

How can you put five cereal packets together to make different shapes if you must put them face-to-face?