Frogs
Age 11 to 14
Challenge Level
How many moves does it take to swap over some red and blue frogs? Do you have a method?
Squares in Rectangles
Age 11 to 14
Challenge Level
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?
Elevenses
Age 11 to 14
Challenge Level
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Tower of Hanoi
Age 11 to 14
Challenge Level
The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
Partly Painted Cube
Age 14 to 16
Challenge Level
Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?
A Little Light Thinking
Age 14 to 16
Challenge Level
Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?
Charlie's Delightful Machine
Age 11 to 16
Challenge Level
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
NRICH is part of the family of activities in the Millennium Mathematics Project.