Triangle numbers

problem

Speedy summations

Age

16 to 18

Challenge level

Watch the video to see how to add together an arithmetic sequence of numbers efficiently.
problem
Favourite

Summing consecutive numbers

Age

11 to 14

Challenge level

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
problem
Favourite

Light the lights again

Age

7 to 11

Challenge level

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you work out the rule for each light?
problem
Favourite

Handshakes

Age

11 to 14

Challenge level

Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
problem
Favourite

Mystic rose

Age

14 to 16

Challenge level

Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
problem

Triangular clock

Age

11 to 14

Challenge level

Trinni rearanges numbers on a clock face so each adjacent pair add up to a triangle number... What number did she put where 6 would usually be?
problem
Favourite

Triangle numbers

Age

11 to 14

Challenge level

Take a look at the multiplication square. The first eleven triangle numbers have been identified. Can you see a pattern? Does the pattern continue?
problem
Favourite

Route to infinity

Age

11 to 14

Challenge level

Can you describe this route to infinity? Where will the arrows take you next?
problem
Favourite

Factors and multiples puzzle

Age

11 to 14

Challenge level

Using your knowledge of the properties of numbers, can you fill all the squares on the board?
problem
Favourite

Take ten sticks

Age

11 to 16

Challenge level

Take ten sticks in heaps any way you like. Make a new heap using one from each of the heaps. By repeating that process could the arrangement 7 - 1 - 1 - 1 ever turn up, except by starting with it?