Working systematically

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

What is the smallest perfect square that ends with the four digits 9009?

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?