Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

Weekly Problem 46 - 2011

Multiply a sequence of n terms together. Can you work out when this product is equal to an integer?

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

Weekly Problem 20 - 2013

Can you calculate the answer to a large sum?

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.

This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.

Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?

Weekly Problem 28 - 2014

What is the units digit of the given expression?

Weekly Problem 30 - 2014

What is the value of $2006 \times 2008 - 2007 \times 2007$?

Weekly Problem 37 - 2014

Which of the five diagrams below could be drawn without taking the pen off the page and without drawing along a line already drawn?

Weekly Problem 1 - 2016

What is the last-but-one digit of 99! ?

Weekly Problem 5 - 2017

Each digit of a positive integer is 1, 2 or 3, and each of these occurs at least twice. What is the smallest such integer that is not divisible by 2 or 3?

Weekly Problem 31 - 2017

The triangle HIJ has the same area as the square FGHI. What is the distance from J to the line extended through F and G?