Try grouping the dominoes in the ways described. Are there any left
over each time? Can you explain why?
Have a good look at these images. Can you describe what is
happening? There are plenty more images like this on NRICH's
Exploring Squares CD.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?
Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?
Kaia is sure that her father has worn a particular tie twice a week
in at least five of the last ten weeks, but her father disagrees.
Who do you think is right?
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.
NRICH has always had good solutions from Madras College in St
Andrew's, Scotland but the solutions to this problem were truly
A new problem posed by Lyndon Baker who has devised many NRICH
problems over the years.
Nick Lord says "This problem encapsulates for me the best features
of the NRICH collection."
Contributions from three different schools helped to solve this
Rhiannon found that multiples of 3 are the key to this problem.
It looks like we may have some budding bellringers in our midst.
This article, written for teachers, looks at the different kinds of
recordings encountered in Primary Mathematics lessons and the
importance of not jumping to conclusions!
Can you beat the computer in the challenging strategy game?
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.
Professor Korner has generously supported school mathematics for more than 30 years and has been a good friend to NRICH since it started.