Problems
Growing Garlic
Stage: 1 Challenge Level: 
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
Street Sequences
Stage: 1 and 2 Challenge Level:
Investigate what happens when you add house numbers along a street in different ways.
Multiplication Square Jigsaw
Stage: 2 Challenge Level:
Can you complete this jigsaw of the multiplication square?
Multiples Grid
Stage: 2 Challenge Level:
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
Factor-multiple Chains
Stage: 2 Challenge Level:
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Route to Infinity
Stage: 3 Challenge Level:
Take some time to look at the route the arrows follow in this diagram. Through how many points does the route pass before it reaches the point (9,4)?
Triangle Numbers
Stage: 3 Challenge Level:
Take a look at the multiplication square. The first eleven triangle numbers have been identified. Can you see a pattern? Does the pattern continue?
Cunning Card Trick
Stage: 3 Challenge Level:
Delight your friends with this cunning trick! Can you explain how it works?
Twizzles Venture Forth
Stage: 4 Challenge Level:
Where we follow twizzles to places that no number has been before.
Twizzle Wind Up
Stage: 4 Challenge Level:
A loopy exploration of z^2+1=0 (z squared plus one) with an eye on winding numbers. Try not to get dizzy!
Twizzle Twists
Stage: 4 Challenge Level:
Make the twizzle twist on its spot and so work out the hidden link.
Tens
Stage: 5 Challenge Level:
When is 7^n + 3^n a multiple of 10? Can you prove the result by two different methods?
Elsewhere...
Featured Solutions
Peg Rotation
Jamie and Nik described these transformations very clearly. However the triangular challenges are still to be cracked!
Mirror, Mirror...
We've received a clear solution to this problem from Alice, George, Kyle, Tom, Nell and Alex.
Articles & Games
Digital Roots
In this article for teachers, Bernard Bagnall describes how to find digital roots and suggests that they can be worth exploring when confronted by a sequence of numbers.
A Story about Absolutely Nothing
This article for the young and old talks about the origins of our number system and the important role zero has to play in it.
Integrated Product Sudoku
This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.
Infinity Is Not a Number - It's a Free Man
Infinity is not a number, and trying to treat it as one tends to be a pretty bad idea. At best you're likely to come away with a headache, at worse the firm belief that 1 = 0. This article discusses the different types of infinity.
The Chinese Remainder Theorem
In this article we shall consider how to solve problems such as "Find all integers that leave a remainder of 1 when divided by 2, 3, and 5."
