article
Modulus Arithmetic and a Solution to Differences
Peter Zimmerman, a Year 13 student at Mill Hill County High School
in Barnet, London wrote this account of modulus arithmetic.
Odd and even numbers
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articleImpossible Sandwiches
In this 7-sandwich: 7 1 3 1 6 4 3 5 7 2 4 6 2 5 there are 7 numbers between the 7s, 6 between the 6s etc. The article shows which values of n can make n-sandwiches and which cannot. -
articleMultiplication Series: Number Arrays
This article for teachers describes how number arrays can be a useful representation for many number concepts. -
articleAll Is Number
Read all about Pythagoras' mathematical discoveries in this article written for students.
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articleTake One Example
This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure. -
problemSummats Clear
Age16 to 18Challenge level
Find the sum, f(n), of the first n terms of the sequence: 0, 1, 1, 2, 2, 3, 3........p, p, p +1, p + 1,..... Prove that f(a + b) - f(a - b) = ab. -
problemArrangements
Age7 to 11Challenge level
Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....? -
problemScore
Age11 to 14Challenge level
There are exactly 3 ways to add 4 odd numbers to get 10. Find all the ways of adding 8 odd numbers to get 20. To be sure of getting all the solutions you will need to be systematic. What about a total of 15 with 6 odd numbers? -
problemComparing Continued Fractions
Age16 to 18Challenge level
Which of these continued fractions is bigger and why? -
problemJenny's Logic
Age11 to 14Challenge level
Weekly Problem 52 - 2009
How did Jenny figure out that Tom's cards added to an even number?