Choose the Mean
Age 11 to 14 Short
Challenge Level
Find 4 numbers which have a mean of 7, a median of 8 and a mode of 9.
Rough Rectangle
Age 11 to 14 Short
Challenge Level
What is the smallest possible area that this rectangle could have?
2014 Even Numbers
Age 11 to 14 Short
Challenge Level
What is the difference between the sum of the first 2014 odd numbers and the sum of the first 2014 even numbers?
Split Clock Face
Age 11 to 14 Short
Challenge Level
Use 2 straight lines to split the clock face into 3 parts so that the sums of the numbers in each of the parts are equal.
Rotation Identification
Age 11 to 14 Short
Challenge Level
Which of these can be obtained by rotating this shape?
Cuboid Faces
Age 11 to 14 Short
Challenge Level
Can you find the volume of a cuboid, given the areas of its faces?
Brothers and Sisters
Age 11 to 14 Short
Challenge Level
Can you work out how many brothers and sisters are in the family?
Missing Digits
Age 11 to 14 Short
Challenge Level
Can you find the missing digits in this calculation?
Range of Averages
Age 11 to 14 Short
Challenge Level
Find these 4 numbers, given their mode, median and range.
Multiplication Cube
Age 11 to 14 Short
Challenge Level
The net shown is folded up to form a cube. What is the largest possible vertex product?
Draining a Pool
Age 11 to 14 Short
Challenge Level
The water is being drained from a pool. After how long will the depth of the pool be 144 cm?
Speed over a Bridge
Age 11 to 14 Short
Challenge Level
How fast is the train travelling as it goes over the bridge?
Overlapping Beer Mats
Age 11 to 14 Short
Challenge Level
Can you find the area of the overlap when these two beer mats are placed on top of each other?
Reverse Ages
Age 11 to 14 Short
Challenge Level
When is the next time that Brian's age will be the reverse of his father's age?
Sum and Differences
Age 11 to 14 Short
Challenge Level
Three numbers add up to 100. The difference between the larger two is 12 and the difference between the smaller two is 2. What are the numbers?
Giant Rubik's Cube
Age 11 to 14 Short
Challenge Level
How many cubes would be visible in a 12 by 12 by 12 Rubik’s cube?
Identical Digit Multiplication
Age 11 to 14 Short
Challenge Level
77 is multiplied by another two-digit number with identical digits. What is the product?
Adding and Multiplying
Age 11 to 14 Short
Challenge Level
Amy misread a question and got an incorrect answer. What should the answer have be?
Square Within a Square Within...
Age 11 to 14 Short
Challenge Level
What fraction of this square is shaded?
Hot Dogs
Age 11 to 14 Short
Challenge Level
How many hot dogs did this hot dog lover eat on the first day of her binge?
Divisible Digits
Age 11 to 14 Short
Challenge Level
Can you find the missing digits, given that the number is divisible by 3, 4, 5 and 6?
Strange Dice
Age 11 to 14 Short
Challenge Level
If two of these unusually numbered dice are thrown, how many different sums are possible?
Bouncing Ball
Age 11 to 14 Short
Challenge Level
A ball is dropped from a height, and every time it hits the ground, it bounces to 3/5 of the height from which it fell.
The Average Age
Age 11 to 14 Short
Challenge Level
Given this information about averages, find the ages of these teachers.
Tile Border
Age 11 to 14 Short
Challenge Level
What is the largest possible number of yellow tiles in this pattern?
Dividing a Square
Age 11 to 14 Short
Challenge Level
A square is divided into three shapes which all have equal areas. Can you find the length of this side?
Roses and Carnations
Age 11 to 14 Short
Challenge Level
How many different bunches of flowers can this class buy for their teacher?
Linear Area
Age 11 to 14 Short
Challenge Level
Find the area of the triangle enclosed by these lines.
Tilted Tank
Age 11 to 14 Short
Challenge Level
Can you find the height of the water in this tilted tank when it is flat?
Packing Small Boxes
Age 11 to 14 Short
Challenge Level
How many small boxes will fit inside the big box?
Graph Area
Age 11 to 14 Short
Challenge Level
Can you find the area between this graph and the x-axis, between x=3 and x=7?
Adding in Pairs
Age 11 to 14 Short
Challenge Level
These are the results when 3 numbers were added in pairs. What were the numbers?
Multiplication Mistake
Age 11 to 14 Short
Challenge Level
Jane accidentally multiplied by 54 instead of 45, and her answer was 198 too big. What number did she multiply 54 by?
Tiled Floor
Age 11 to 14 Short
Challenge Level
This tiled floor has 109 purple tiles. How many tiles are there altogether?
Clubs
Age 11 to 14 Short
Challenge Level
How many students are in the maths club and the science club?
Palindromic Milometer
Age 11 to 14 Short
Challenge Level
At the beginning and end of Alan's journey, his milometer showed a palindromic number. Can you find his maximum possible average speed?
Missing 9s
Age 11 to 14 Short
Challenge Level
Sara makes a list of the whole numbers that do not contain any 9s. What is the 300th number on her list?
Lattice Points on a Line
Age 11 to 14 Short
Challenge Level
How many lattice points are there in the first quadrant that lie on the line 3x + 4y = 59 ?
Diagonal Side
Age 11 to 14 Short
Challenge Level
Can you work out the area of a square drawn on a diagonal?
The Elephant Diet
Age 11 to 14 Short
Challenge Level
Use the relationship between the elephant and the rabbit to find out how many carrots the rabbit eats in a day
Shifting Average
Age 11 to 14 Short
Challenge Level
What happens to the average if you subtract 8 from all of the numbers?
Average Temperature
Age 11 to 14 Short
Challenge Level
The average temperature of six cities is 5$^\circ$C. What is the average temperature when two cities are added?
Between a Sixth and a Twelfth
Age 11 to 14 Short
Challenge Level
The space on a number line between a sixth and a twelfth is split into 3 equal parts. Find the number indicated.
Square Grid
Age 11 to 14 Short
Challenge Level
Can you work out what fraction of this grid is shaded?
Red Card Blue Card
Age 11 to 14 Short
Challenge Level
Can you arrange the red and blue cards so that the rules are all followed?
Add All the Angles
Age 11 to 14 Short
Challenge Level
Find the sum of all of the angles denoted by letters in this diagram
Number of Arms
Age 11 to 14 Short
Challenge Level
What is the probability that the next person you meet has an above average number of arms?
Leap Monday
Age 11 to 14 Short
Challenge Level
Can you find the next time that the 29th of February will fall on a Monday?
Committees
Age 11 to 14 Short
Challenge Level
Every member of the club is a member of two committees. How many members are there in the club?
Clock Angle
Age 11 to 14 Short
Challenge Level
What is the angle between the the hands of a clock at 8:24?
Washing Elephants
Age 11 to 14 Short
Challenge Level
How long will it take Mary and Nigel to wash an elephant if they work together?
Last Digit
Age 11 to 14 Short
Challenge Level
What is the last digit in this calculation involving powers?
Black and Gold Storeys
Age 11 to 14 Short
Challenge Level
25 of the storeys of a 50 storey building are painted gold, and the rest are painted black...
Divisible by 55
Age 11 to 14 Short
Challenge Level
Choose the digits $a$ and $b$ so that this number is divisible by 55.
Tricky Fractions
Age 11 to 14 Short
Challenge Level
Use this series of fractions to find the value of x.
Which Face?
Age 14 to 16 Short
Challenge Level
Which faces are opposite each other when this net is folded into a cube?
Mean Balance
Age 14 to 16 Short
Challenge Level
Given information about the mean, can you work out the missing numbers?
Flipping Coins
Age 14 to 16 Short
Challenge Level
A coin is flipped 4 times. What is the probability of getting heads at least 3 times?
Bobbly Perimeter
Age 14 to 16 Short
Challenge Level
Find the perimeter of this shape made of semicircles
Ratio of Areas
Age 14 to 16 Short
Challenge Level
What is the ratio of the area of the hexagon to the area of the triangle?
Swapping Sweets
Age 14 to 16 Short
Challenge Level
If two girls each take a sweet from each other's bags, what is the probability that they end up with what they started with?
Length, Width and Area
Age 14 to 16 Short
Challenge Level
The area of a rectangle is 225 square units. Find its width.
Table Total
Age 14 to 16 Short
Challenge Level
Can you find the sum of all of the numbers in the table?
Powerful Expressions
Age 14 to 16 Short
Challenge Level
Put these expressions in order, from smallest to largest.
Growing Triangle
Age 14 to 16 Short
Challenge Level
If the base and height of a triangle are increased by different percentages, what happens to its area?
Diagonal Area
Age 14 to 16 Short
Challenge Level
A square has area 72 cm$^2$. Find the length of its diagonal.
Three Right Angles
Age 14 to 16 Short
Challenge Level
Work your way through these right-angled triangles to find $x$.
XOXOXO
Age 14 to 16 Short
Challenge Level
6 tiles are placed in a row. What is the probability that no two adjacent tiles have the same letter on them?
Square in a Circle in a Square
Age 14 to 16 Short
Challenge Level
What is the ratio of the areas of the squares in the diagram?
Strike a Chord
Age 14 to 16 Short
Challenge Level
Can you work out the radius of a circle from some information about a chord?
Dolly Dolphin
Age 14 to 16 Short
Challenge Level
Can you find Dolly Dolphin's average speed as she swims with and against the current?
Doubly Isosceles
Age 14 to 16 Short
Challenge Level
Find the missing distance in this diagram with two isosceles triangles
Maximum Mean
Age 14 to 16 Short
Challenge Level
What is the largest that the mean of these numbers could be?
Black and White Socks
Age 14 to 16 Short
Challenge Level
There are 20 black socks and some white socks in a drawer. Can you work out how many of the socks are white?
Snapped Palm Tree
Age 14 to 16 Short
Challenge Level
A palm tree has snapped in a storm. What is the height of the piece that is still standing?
Hexagon Perimeter
Age 14 to 16 Short
Challenge Level
A circle of radius 1 is inscribed in a regular hexagon. What is the perimeter of the hexagon?
Photocopied Map
Age 14 to 16 Short
Challenge Level
What will the scale on this map be after it has been photocopied?
3-4-5 Circle
Age 14 to 16 Short
Challenge Level
Can you find the radius of the circle inscribed inside a '3-4-5 triangle'?
Square to a Rectangle
Age 14 to 16 Short
Challenge Level
Kevin has moved some tiles to change the shape of his patio from a square to a rectangle. What are the lengths of the sides of the rectangle?
Inches and Barleycorns
Age 14 to 16 Short
Challenge Level
How many barleycorns are there in one inch?
NRICH is part of the family of activities in the Millennium Mathematics Project.