Network Trees
Age 14 to 18
Challenge Level
Explore some of the different types of network, and prove a result about network trees.
Maxi Pyramid
Age 11 to 16
Challenge Level
What is the largest number you can obtain at the top of this pyramid?
River Crossing
Age 11 to 18
Challenge Level
There is nothing half so much worth doing as simply messing about in boats...
Isosceles Seven
Age 14 to 16
Challenge Level
Is it possible to find the angles in this rather special isosceles triangle?
Iffy Logic
Age 14 to 18
Challenge Level
Can you rearrange the cards to make a series of correct mathematical statements?
The Tour De Clochemerle
Age 14 to 18
Challenge Level
Can you work out where these 5 riders came in a not-quite-so-famous bike race?
Circumference Angles
Age 11 to 16
Challenge Level
Can you prove the angle properties described by some of the circle theorems?
Cyclic Quadrilaterals Proof
Age 11 to 16
Challenge Level
Can you prove that the opposite angles of cyclic quadrilaterals add to $180^\circ$?
Pythagoras Proofs
Age 11 to 16
Challenge Level
Can you make sense of these three proofs of Pythagoras' Theorem?
Matter of Scale
Age 14 to 16
Challenge Level
Can you prove Pythagoras' Theorem using enlargements and scale factors?
Overlap
Age 14 to 16
Challenge Level
A red square and a blue square overlap. Is the area of the overlap always the same?
Pentakite
Age 14 to 18
Challenge Level
Given a regular pentagon, can you find the distance between two non-adjacent vertices?
Quad in Quad
Age 14 to 18
Challenge Level
Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?
NRICH is part of the family of activities in the Millennium Mathematics Project.