Number Sandwiches
Age 7 to 14
Challenge Level
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
Three Neighbours
Age 7 to 14
Challenge Level
Take three consecutive numbers and add them together. What do you notice?
Fruity Totals
Age 7 to 16
Challenge Level
In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?
Summing Consecutive Numbers
Age 11 to 14
Challenge Level
15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
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?
Diminishing Returns
Age 11 to 14
Challenge Level
How much of the square is coloured blue? How will the pattern continue?
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?
What Numbers Can We Make?
Age 11 to 14
Challenge Level
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Magic Letters
Age 11 to 14
Challenge Level
Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
Route to Infinity
Age 11 to 14
Challenge Level
Can you describe this route to infinity? Where will the arrows take you next?
Seven Squares
Age 11 to 14
Challenge Level
Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
Always a Multiple?
Age 11 to 14
Challenge Level
Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...
1 Step 2 Step
Age 11 to 14
Challenge Level
Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?
What's it Worth?
Age 11 to 16
Challenge Level
There are lots of different methods to find out what the shapes are worth - how many can you find?
Adding Odd Numbers
Age 11 to 16
Challenge Level
Is there a quick and easy way to calculate the sum of the first 100 odd numbers?
Where Are the Primes?
Age 11 to 16
Challenge Level
What can we say about all the primes which are greater than 3?
Arithmagons
Age 11 to 16
Challenge Level
Can you find the values at the vertices when you know the values on the edges?
Three Consecutive Odd Numbers
Age 11 to 16
Challenge Level
How many sets of three consecutive odd numbers can you find, in which all three numbers are prime?
Take Three from Five
Age 11 to 16
Challenge Level
Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?
Marbles in a Box
Age 11 to 16
Challenge Level
How many winning lines can you make in a three-dimensional version of noughts and crosses?
What Does it All Add up To?
Age 11 to 18
Challenge Level
If you take four consecutive numbers and add them together, the answer will always be even. What else do you notice?
Different Products
Age 14 to 16
Challenge Level
Take four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
Factorising with Multilink
Age 14 to 16
Challenge Level
Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?
What's Possible?
Age 14 to 16
Challenge Level
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
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?
Attractive Tablecloths
Age 14 to 16
Challenge Level
Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
Latin Numbers
Age 14 to 16
Challenge Level
Can you create a Latin Square from multiples of a six digit number?
Impossible Sums
Age 14 to 18
Challenge Level
Which numbers cannot be written as the sum of two or more consecutive numbers?
Difference of Odd Squares
Age 14 to 18
Challenge Level
$40$ can be written as $7^2 - 3^2.$ Which other numbers can be written as the difference of squares of odd numbers?
Integration Matcher
Age 16 to 18
Challenge Level
Can you match the charts of these functions to the charts of their integrals?
Prime Sequences
Age 16 to 18
Challenge Level
This group tasks allows you to search for arithmetic progressions in the prime numbers. How many of the challenges will you discover for yourself?
Stats Statements
Age 16 to 18
Challenge Level
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Impossible Triangles?
Age 16 to 18
Challenge Level
Which of these triangular jigsaws are impossible to finish?
What's a Group?
Age 16 to 18
Challenge Level
Explore the properties of some groups such as: The set of all real numbers excluding -1 together with the operation x*y = xy + x + y. Find the identity and the inverse of the element x.
NRICH is part of the family of activities in the Millennium Mathematics Project.