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
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
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
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
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
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
Route to infinity

Age

11 to 14

Challenge level

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