Working systematically

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!

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

Find the positive integer solutions of the equation (1+1/a)(1+1/b)(1+1/c) = 2

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

Your partner chooses two beads and places them side by side behind a screen. What is the minimum number of guesses you would need to be sure of guessing the two beads and their positions?

In how many distinct ways can six islands be joined by bridges so that each island can be reached from every other island...