Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
In this town, houses are built with one room for each person. There
are some families of seven people living in the town. In how many
different ways can they build their houses?
What is the least number of moves you can take to rearrange the
bears so that no bear is next to a bear of the same colour?
What happens to the area of a square if you double the length of
the sides? Try the same thing with rectangles, diamonds and other
shapes. How do the four smaller ones fit into the larger one?
Investigate the area of 'slices' cut off this cube of cheese. What
would happen if you had different-sized block of cheese to start
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
What happens if you join every second point on this circle? How
about every third point? Try with different steps and see if you
can predict what will happen.
In how many ways can you fit all three pieces together to make
shapes with line symmetry?
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?
A circular plate rolls in contact with the sides of a rectangular
tray. How much of its circumference comes into contact with the
sides of the tray when it rolls around one circuit?
A picture is made by joining five small quadrilaterals together to
make a large quadrilateral. Is it possible to draw a similar
picture if all the small quadrilaterals are cyclic?
A polite number can be written as the sum of two or more
consecutive positive integers. Find the consecutive sums giving the
polite numbers 544 and 424. What characterizes impolite numbers?
It is believed that weaker snooker players have a better chance of
winning matches over eleven frames (i.e. first to win 6 frames)
than they do over fifteen frames. Is this true?
Can you find the solution to this algebraic inequality?
A circular plate rolls inside a rectangular tray making five
circuits and rotating about its centre seven times. Find the
dimensions of the tray.
How can we decide what the 'best' solution to this problem is? Take
a look at these and make up your own mind!
Jacob worked really hard on this investigation.
We received many good solutions, insights and explanations to this
Abinhav used algebra to explain his ideas about this problem.
This article is based on some of the ideas that emerged during the production of a book which takes visualising as its focus. We began to identify problems which helped us to take a structured view of the purposes and skills of visualising.
The aim of the game is to slide the green square from the top right
hand corner to the bottom left hand corner in the least number of
Start with a large square, join the midpoints of its sides, you'll see four right angled triangles. Remove these triangles, a second square is left. Repeat the operation. What happens?
Sharon Walter, an NRICH teacher fellow, talks about her experiences
of trying to embed NRICH tasks into her everyday practice.
Two sudokus in one. Challenge yourself to make the necessary
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.