Air Nets
Age 7 to 18
Challenge Level
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
Diamond Collector
Age 11 to 16
Challenge Level
Collect as many diamonds as you can by drawing three straight lines.
Nine Colours
Age 11 to 16
Challenge Level
Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
Marbles in a Box
Age 11 to 16
Challenge Level
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Pick's Theorem
Age 14 to 16
Challenge Level
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.
Painted Purple
Age 14 to 16 Short
Challenge Level
Three faces of a $3 \times 3$ cube are painted red, and the other three are painted blue. How many of the 27 smaller cubes have at least one red and at least one blue face?
Painted Cube
Age 14 to 16
Challenge Level
Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
Newspaper Sheets
Age 14 to 16 Short
Challenge Level
From only the page numbers on one sheet of newspaper, can you work out how many sheets there are altogether?
Out of the Window
Age 14 to 16 Short
Challenge Level
Find out how many pieces of hardboard of differing sizes can fit through a rectangular window.
Steel Cables
Age 14 to 16
Challenge Level
Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
Building Tetrahedra
Age 14 to 16
Challenge Level
Can you make a tetrahedron whose faces all have the same perimeter?
Twelve Cubed
Age 14 to 16 Short
Challenge Level
A wooden cube with edges of length 12cm is cut into cubes with edges of length 1cm. What is the total length of the all the edges of these centimetre cubes?
In or Out?
Age 14 to 16 Short
Challenge Level
Weekly Problem 52 - 2014
Four arcs are drawn in a circle to create a shaded area. What fraction of the area of the circle is shaded?
Dicey Directions
Age 14 to 16 Short
Challenge Level
An ordinary die is placed on a horizontal table with the '1' face facing East... In which direction is the '1' face facing after this sequence of moves?
Trisected Triangle
Age 14 to 16 Short
Challenge Level
Weekly Problem 34 - 2015
Four tiles are given. For which of them can three be placed together to form an equilateral triangle?
Semicircular Design
Age 14 to 16 Short
Challenge Level
Weekly Problem 9 - 2016
The diagram to the right shows a logo made from semi-circular arcs. What fraction of the logo is shaded?
Attractive Tablecloths
Age 14 to 16
Challenge Level
Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
Vector Journeys
Age 14 to 18
Challenge Level
Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?
Coordinated Crystals
Age 16 to 18
Challenge Level
Explore the lattice and vector structure of this crystal.
NRICH is part of the family of activities in the Millennium Mathematics Project.