Does a graph of the triangular numbers cross a graph of the six
times table? If so, where? Will a graph of the square numbers cross
the times table too?
A challenge that requires you to apply your knowledge of the
properties of numbers. Can you fill all the squares on the board?
Each light in this interactivity turns on according to a rule. What
happens when you enter different numbers? Can you find the smallest
number that lights up all four lights?
Sam sets up displays of cat food in his shop in triangular stacks.
If Felix buys some, then how can Sam arrange the remaining cans in
Complete the magic square using the numbers 1 to 25 once each. Each
row, column and diagonal adds up to 65.
I have forgotten the number of the combination of the lock on my
briefcase. I did have a method for remembering it...
Can you find an efficient method to work out how many handshakes
there would be if hundreds of people met?
These alphabet bricks are painted in a special way. A is on one
brick, B on two bricks, and so on. How many bricks will be painted
by the time they have got to other letters of the alphabet?
Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
Triangle numbers can be represented by a triangular array of
squares. What do you notice about the sum of identical triangle
Take a look at the multiplication square. The first eleven triangle
numbers have been identified. Can you see a pattern? Does the
Sam displays cans in 3 triangular stacks. With the same number he
could make one large triangular stack or stack them all in a square
based pyramid. How many cans are there how were they arranged?
Here is a collection of puzzles about Sam's shop sent in by club
members. Perhaps you can make up more puzzles, find formulas or
find general methods.
Can you describe this route to infinity? Where will the arrows take you next?