Working systematically

Label this plum tree graph to make it totally magic!

Show there are exactly 12 magic labellings of the Magic W using the numbers 1 to 9. Prove that for every labelling with a magic total T there is a corresponding labelling with a magic total 30-T.

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?

Squares of the type shown are sewn together to make a quilt. How many different quilts can be made?

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?

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

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.