Working systematically

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?

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

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

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?

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 16 - 2016
How many three digit numbers have the property that the middle digit is the mean of the other two digits?

Design an arrangement of display boards in the school hall which fits the requirements of different people.

There is nothing half so much worth doing as simply messing about in boats...