Working systematically

problem
Counting on letters

Age

11 to 14

Challenge level

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?
problem
Purr-fection

Age

16 to 18

Challenge level

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

Age

14 to 18

Challenge level

Label this plum tree graph to make it totally magic!
problem
W mates

Age

16 to 18

Challenge level

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.
problem
Cayley

Age

11 to 14

Challenge level

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
problem
Football crazy hockey mad

Age

11 to 14

Challenge level

In a league of 5 football teams which play in a round robin tournament show that it is possible for all five teams to be league leaders.
problem
1 to 8

Age

7 to 11

Challenge level

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
problem
Ancient runes

Age

7 to 11

Challenge level

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?
problem
Smith and Jones

Age

14 to 16

Challenge level

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!
problem
Satnav dilemma

Age

11 to 14

Challenge level

How many routes are there in this diagram from S to T?