Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
You have 27 small cubes, 3 each of nine colours. Use the small
cubes to make a 3 by 3 by 3 cube so that each face of the bigger
cube contains one of every colour.
Starting with four different triangles, imagine you have an
unlimited number of each type. How many different tetrahedra can
you make? Convince us you have found them all.
Ever thought of playing three dimensional Noughts and Crosses? This problem might help you visualise what's involved.
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Three people chose this as a favourite problem. It is the sort of
problem that needs thinking time - but once the connection is made
it gives access to many similar ideas.
Libby Jared helped to set up NRICH and this is one of her favourite
problems. It's a problem suitable for a wide age range and best
Lyndon chose this as one of his favourite problems. It is
accessible but needs some careful analysis of what is included and
what is not. A systematic approach is really helpful.
It looks like we may have some budding bellringers in our midst.
Go to last month's problems to see more solutions.
Toni Beardon has chosen this article introducing a rich area for
practical exploration and discovery in 3D geometry
Alf Coles writes about how he tries to create 'spaces for
exploration' for the students in his classrooms.
A Sudoku with clues as ratios.