Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Think of a number... follow the machine's instructions. I know what your number is! Can you explain how I know?
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
Three frogs started jumping randomly over any adjacent frog. Is it possible for them to finish up in the same order they started?
Weekly Problem 37 - 2011
Rotating a pencil twice about two different points gives surprising results...
The sums of the squares of three related numbers is also a perfect square - can you explain why?
Using a ruler, pencil and compasses only, it is possible to construct a square inside any triangle so that all four vertices touch the sides of the triangle.