Working systematically

problem

Approaching Midnight: Changing Smallest Step

Age

7 to 14

Liz played Approaching Midnight and wondered how changing the smallest step size affects the game.
problem

Central Sum

Age

11 to 14

Challenge level

Can you find numbers between 100 and 999 that have a middle digit equal to the sum of the other two digits?
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

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

Satnav Dilemma

Age

11 to 14

Challenge level

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

Negative Dice

Age

11 to 14

Challenge level

If the odd numbers on two dice are made negative, which of the totals cannot be achieved?
problem

Nine, Ten and One

Age

11 to 14

Challenge level

Can you find the value of t in these equations?