How Old Am I?
Age 14 to 16
Challenge Level
In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?
Funny Factorisation
Age 11 to 16
Challenge Level
Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?
Where Can We Visit?
Age 11 to 14
Challenge Level
Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?
Two and Two
Age 11 to 16
Challenge Level
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
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?
In a Box
Age 14 to 16
Challenge Level
Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?
Triangles to Tetrahedra
Age 11 to 14
Challenge Level
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
Frogs
Age 11 to 14
Challenge Level
How many moves does it take to swap over some red and blue frogs? Do you have a method?
Shady Symmetry
Age 11 to 14
Challenge Level
How many different symmetrical shapes can you make by shading triangles or squares?
Hexy-metry
Age 14 to 16
Challenge Level
A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?
Special Numbers
Age 11 to 14
Challenge Level
My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?
The Spider and the Fly
Age 14 to 16
Challenge Level
A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?
Cuboids
Age 11 to 14
Challenge Level
Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
On the Edge
Age 11 to 14
Challenge Level
If you move the tiles around, can you make squares with different coloured edges?
Square It
Age 11 to 16
Challenge Level
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
Isosceles Triangles
Age 11 to 14
Challenge Level
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
Stars
Age 11 to 14
Challenge Level
Can you work out what step size to take to ensure you visit all the dots on the circle?
Arithmagons
Age 11 to 16
Challenge Level
Can you find the values at the vertices when you know the values on the edges?
Quadrilaterals Game
Age 11 to 14
Challenge Level
A game for 2 or more people, based on the traditional card game Rummy.
Shapely Pairs
Age 11 to 14
Challenge Level
A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...
Property Chart
Age 11 to 14
Challenge Level
A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?
Two's Company
Age 11 to 14
Challenge Level
Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?
Cosy Corner
Age 11 to 14
Challenge Level
Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?
Semi-regular Tessellations
Age 11 to 16
Challenge Level
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
Product Sudoku
Age 11 to 16
Challenge Level
The clues for this Sudoku are the product of the numbers in adjacent squares.
Substitution Cipher
Age 11 to 14
Challenge Level
Find the frequency distribution for ordinary English, and use it to help you crack the code.
Transformation Game
Age 11 to 14
Challenge Level
Why not challenge a friend to play this transformation game?
A Chance to Win?
Age 11 to 14
Challenge Level
Imagine you were given the chance to win some money... and imagine you had nothing to lose...
Difference Sudoku
Age 14 to 16
Challenge Level
Use the differences to find the solution to this Sudoku.
Which Spinners?
Age 14 to 18
Challenge Level
Can you work out which spinners were used to generate the frequency charts?
M, M and M
Age 11 to 14
Challenge Level
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
Treasure Hunt
Age 7 to 14
Challenge Level
Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?
The Remainders Game
Age 7 to 14
Challenge Level
Play this game and see if you can figure out the computer's chosen number.
Nice or Nasty
Age 7 to 14
Challenge Level
There are nasty versions of this dice game but we'll start with the nice ones...
Dicey Operations
Age 11 to 14
Challenge Level
Who said that adding, subtracting, multiplying and dividing couldn't be fun?
How Much Can We Spend?
Age 11 to 14
Challenge Level
A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?
Tower of Hanoi
Age 11 to 14
Challenge Level
The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
Shifting Times Tables
Age 11 to 14
Challenge Level
Can you find a way to identify times tables after they have been shifted up or down?
A Little Light Thinking
Age 14 to 16
Challenge Level
Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?
Charlie's Delightful Machine
Age 11 to 16
Challenge Level
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Sociable Cards
Age 11 to 14
Challenge Level
Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?
Last One Standing
Age 14 to 16
Challenge Level
Imagine a room full of people who keep flipping coins until they get a tail. Will anyone get six heads in a row?
What Does Random Look Like?
Age 11 to 14
Challenge Level
Engage in a little mathematical detective work to see if you can spot the fakes.
Which Solids Can We Make?
Age 11 to 14
Challenge Level
Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?
Missing Multipliers
Age 7 to 14
Challenge Level
What is the smallest number of answers you need to reveal in order to work out the missing headers?
Multiplication Arithmagons
Age 14 to 16
Challenge Level
Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?
Finding Factors
Age 14 to 16
Challenge Level
Can you find the hidden factors which multiply together to produce each quadratic expression?
Constructing Triangles
Age 11 to 14
Challenge Level
Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?
Perception Versus Reality
Age 14 to 18
Challenge Level
Infographics are a powerful way of communicating statistical information. Can you come up with your own?
Wipeout
Age 11 to 16
Challenge Level
Can you do a little mathematical detective work to figure out which number has been wiped out?
Box Plot Match
Age 14 to 16
Challenge Level
Match the cumulative frequency curves with their corresponding box plots.
Forwards Add Backwards
Age 11 to 14
Challenge Level
What happens when you add a three digit number to its reverse?
Reversals
Age 11 to 14
Challenge Level
Where should you start, if you want to finish back where you started?
Unequal Averages
Age 11 to 14
Challenge Level
Play around with sets of five numbers and see what you can discover about different types of average...
Gabriel's Problem
Age 11 to 14
Challenge Level
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
NRICH is part of the family of activities in the Millennium Mathematics Project.