An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP
have equal areas. Prove X and Y divide the sides of PQRS in the
A 1 metre cube has one face on the ground and one face against a
wall. A 4 metre ladder leans against the wall and just touches the
cube. How high is the top of the ladder above the ground?
Here are some different ways in which we can split 100:
The products of these sets are all different:
What is the largest product that can be made from whole numbers that add up to 100?
Choose another starting number and split it in a variety of ways.
What is the largest product this time?
Can you find a strategy for splitting any number so that you always get the largest product?
Click here for a poster of this problem.