Working systematically

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated.

Pentagram Pylons - can you elegantly recreate them? Or, the European flag in LOGO - what poses the greater problem?

Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?

Remember that you want someone following behind you to see where you went. Can yo work out how these patterns were created and recreate them?

Mr Smith and Mr Jones are two maths teachers. By asking questions, the answers to which may be right or wrong, Mr Jones is able to find the number of the house Mr Smith lives in... Or not!

An ordinary die is placed on a horizontal table with the '1' face facing East... In which direction is the '1' face facing after this sequence of moves?

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?

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?

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

Can you match each graph to one of the statements?