Working systematically

problem
Half and half

Age

11 to 14

Challenge level

Two of the four small triangles are to be painted black. In how many ways can this be done?
problem
Threes and fours

Age

14 to 16

Challenge level

What is the smallest integer where every digit is a 3 or a 4 and it is divisible by both 3 and 4?
problem
Isometric rhombuses

Age

11 to 14

Challenge level

Weekly Problem 31 - 2016
The diagram shows a grid of $16$ identical equilateral triangles. How many rhombuses are there made up of two adjacent small triangles?
problem
End of a prime

Age

14 to 16

Challenge level

I made a list of every number that is the units digit of at least one prime number. How many digits appear in the list?
problem
Middle digit mean

Age

11 to 16

Challenge level

Weekly Problem 16 - 2016
How many three digit numbers have the property that the middle digit is the mean of the other two digits?
problem
Growing surprises

Age

11 to 14

Challenge level

Can you find the connections between linear and quadratic patterns?
problem
Completing quadrilaterals

Age

11 to 14

Challenge level

We started drawing some quadrilaterals - can you complete them?
problem
Making a difference

Age

11 to 14

Challenge level

How many different differences can you make?
problem
Display boards

Age

7 to 11

Challenge level

Design an arrangement of display boards in the school hall which fits the requirements of different people.
problem
Six numbered cubes

Age

7 to 11

Challenge level

This task combines spatial awareness with addition and multiplication.