Here is a collection of ours - and Libby's - favourite problems which we have enjoyed both at Cambridge and in the classroom!
problem
One basket or group photo
Age
7 to 18
Challenge level
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
tackled practically.
problem
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?
problem
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?
problem
Factors and multiples puzzle
Age
11 to 14
Challenge level
Using your knowledge of the properties of numbers, can you fill all the squares on the board?
problem
Your number is...
Age
7 to 14
Challenge level
Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know?
problem
Number pyramids
Age
11 to 14
Challenge level
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
problem
Cuboid challenge
Age
11 to 16
Challenge level
What's the largest volume of box you can make from a square of paper?
problem
Tilted squares
Age
11 to 14
Challenge level
It's easy to work out the areas of most squares that we meet, but what if they were tilted?