Working systematically

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
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
A mixed-up clock

Age

7 to 11

Challenge level

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
problem
Fractional triangles

Age

7 to 11

Challenge level

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
problem
Chocs, mints, jellies

Age

7 to 11

Challenge level

In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way to share the sweets between the three children so they each get the kind they like. Is there more than one way to do it?
problem
Farey sequences

Age

11 to 14

Challenge level

There are lots of ideas to explore in these sequences of ordered fractions.
problem
Flipping twisty matrices

Age

14 to 18

Challenge level

Investigate the transformations of the plane given by the 2 by 2 matrices with entries taking all combinations of values 0, -1 and +1.
problem
How many miles to go?

Age

11 to 14

Challenge level

How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?
problem
Adding plus

Age

7 to 11

Challenge level

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?
problem
A square of numbers

Age

7 to 11

Challenge level

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?