The problems in this collection have been adapted from problems that have been set in South East Asian Mathematics Competitions.
problem
Sum and differences
Age
11 to 14
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?
problem
Cuboid faces
Age
11 to 14
Challenge level
Can you find the volume of a cuboid, given the areas of its faces?
problem
Choose the mean
Age
11 to 14
Challenge level
Find 4 numbers which have a mean of 7, a median of 8 and a mode of 9.
problem
Reverse ages
Age
11 to 14
Challenge level
When is the next time that Brian's age will be the reverse of his father's age?
problem
Draining a pool
Age
11 to 14
Challenge level
The water is being drained from a pool. After how long will the depth of the pool be 144 cm?
problem
Adding and multiplying
Age
11 to 14
Challenge level
Amy misread a question and got an incorrect answer. What should the answer have be?
problem
Bouncing ball
Age
11 to 14
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.
problem
Split clock face
Age
11 to 14
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.
problem
Strange dice
Age
11 to 14
Challenge level
If two of these unusually numbered dice are thrown, how many different sums are possible?
problem
Giant Rubik's cube
Age
11 to 14
Challenge level
How many cubes would be visible in a 12 by 12 by 12 Rubik’s cube?
problem
Range of averages
Age
11 to 14
Challenge level
Find these 4 numbers, given their mode, median and range.
problem
Brothers and sisters
Age
11 to 14
Challenge level
Can you work out how many brothers and sisters are in the family?
problem
Missing digits
Age
11 to 14
Challenge level
Can you find the missing digits in this calculation?
problem
Speed over a bridge
Age
11 to 14
Challenge level
How fast is the train travelling as it goes over the bridge?
problem
Rough rectangle
Age
11 to 14
Challenge level
What is the smallest possible area that this rectangle could have?
problem
Hot dogs
Age
11 to 14
Challenge level
How many hot dogs did this hot dog lover eat on the first day of her binge?
problem
Square within a square within...
Age
11 to 14
Challenge level
What fraction of this square is shaded?
problem
Rotation identification
Age
11 to 14
Challenge level
Which of these can be obtained by rotating this shape?
problem
Overlapping beer mats
Age
11 to 14
Challenge level
Can you find the area of the overlap when these two beer mats are placed on top of each other?
problem
Identical digit multiplication
Age
11 to 14
Challenge level
77 is multiplied by another two-digit number with identical digits. What is the product?
problem
Divisible digits
Age
11 to 14
Challenge level
Can you find the missing digits, given that the number is divisible by 3, 4, 5 and 6?
problem
Multiplication cube
Age
11 to 14
Challenge level
The net shown is folded up to form a cube. What is the largest possible vertex product?
problem
2014 even numbers
Age
11 to 14
Challenge level
What is the difference between the sum of the first 2014 odd numbers and the sum of the first 2014 even numbers?
problem
Missing 9s
Age
11 to 14
Challenge level
Sara makes a list of the whole numbers that do not contain any 9s. What is the 300th number on her list?
problem
Red card blue card
Age
11 to 14
Challenge level
Can you arrange the red and blue cards so that the rules are all followed?
problem
Roses and carnations
Age
11 to 14
Challenge level
How many different bunches of flowers can this class buy for their teacher?
problem
Adding in pairs
Age
11 to 14
Challenge level
These are the results when 3 numbers were added in pairs. What were the numbers?
problem
Clubs
Age
11 to 14
Challenge level
How many students are in the maths club and the science club?
problem
The elephant diet
Age
11 to 14
Challenge level
Use the relationship between the elephant and the rabbit to find out how many carrots the rabbit eats in a day
problem
Linear area
Age
11 to 14
Challenge level
Find the area of the triangle enclosed by these lines.
problem
Lattice points on a line
Age
11 to 14
Challenge level
How many lattice points are there in the first quadrant that lie on the line 3x + 4y = 59 ?
problem
Tiled floor
Age
11 to 14
Challenge level
This tiled floor has 109 purple tiles. How many tiles are there altogether?
problem
Diagonal side
Age
11 to 14
Challenge level
Can you work out the area of a square drawn on a diagonal?
problem
Average temperature
Age
11 to 14
Challenge level
The average temperature of six cities is 5$^\circ$C. What is the average temperature when two cities are added?
problem
Graph area
Age
11 to 14
Challenge level
Can you find the area between this graph and the x-axis, between x=3 and x=7?
problem
Between a sixth and a twelfth
Age
11 to 14
Challenge level
The space on a number line between a sixth and a twelfth is split into 3 equal parts. Find the number indicated.
problem
Packing small boxes
Age
11 to 14
Challenge level
How many small boxes will fit inside the big box?
problem
Palindromic milometer
Age
11 to 14
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?
problem
Shifting average
Age
11 to 14
Challenge level
What happens to the average if you subtract 8 from all of the numbers?
problem
Tile border
Age
11 to 14
Challenge level
What is the largest possible number of yellow tiles in this pattern?
problem
Dividing a square
Age
11 to 14
Challenge level
A square is divided into three shapes which all have equal areas. Can you find the length of this side?
problem
Square grid
Age
11 to 14
Challenge level
Can you work out what fraction of this grid is shaded?
problem
Tilted tank
Age
11 to 14
Challenge level
Can you find the height of the water in this tilted tank when it is flat?
problem
The average age
Age
11 to 14
Challenge level
Given this information about averages, find the ages of these teachers.
problem
Multiplication mistake
Age
11 to 14
Challenge level
Jane accidentally multiplied by 54 instead of 45, and her answer was 198 too big. What number did she multiply 54 by?
problem
Committees
Age
11 to 14
Challenge level
Every member of the club is a member of two committees. How many members are there in the club?
problem
Black and gold storeys
Age
11 to 14
Challenge level
25 of the storeys of a 50 storey building are painted gold, and the rest are painted black...
problem
Leap monday
Age
11 to 14
Challenge level
Can you find the next time that the 29th of February will fall on a Monday?
problem
Clock angle
Age
11 to 14
Challenge level
What is the angle between the the hands of a clock at 8:24?
problem
Number of arms
Age
11 to 14
Challenge level
What is the probability that the next person you meet has an above average number of arms?
problem
Add all the angles
Age
11 to 14
Challenge level
Find the sum of all of the angles denoted by letters in this diagram
problem
Last digit
Age
11 to 14
Challenge level
What is the last digit in this calculation involving powers?
problem
Washing elephants
Age
11 to 14
Challenge level
How long will it take Mary and Nigel to wash an elephant if they work together?
problem
Tricky fractions
Age
11 to 14
Challenge level
Use this series of fractions to find the value of x.
problem
Divisible by 55
Age
11 to 14
Challenge level
Choose the digits $a$ and $b$ so that this number is divisible by 55.
problem
Mean balance
Age
14 to 16
Challenge level
Given information about the mean, can you work out the missing numbers?
problem
Megabytes and kilobytes
Age
14 to 16
Challenge level
How many bytes are there in one megabyte?
problem
Flipping coins
Age
14 to 16
Challenge level
A coin is flipped 4 times. What is the probability of getting heads at least 3 times?
problem
Which face?
Age
14 to 16
Challenge level
Which faces are opposite each other when this net is folded into a cube?
problem
Table total
Age
14 to 16
Challenge level
Can you find the sum of all of the numbers in the table?
problem
Swapping sweets
Age
14 to 16
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?
problem
The power of the sum
Age
14 to 16
Challenge level
What is this sum, expressed as a power of 2?
problem
Length, width and area
Age
14 to 16
Challenge level
The area of a rectangle is 225 square units. Find its width.
problem
Ratio of areas
Age
14 to 16
Challenge level
What is the ratio of the area of the hexagon to the area of the triangle?
problem
Bobbly perimeter
Age
14 to 16
Challenge level
Find the perimeter of this shape made of semicircles
problem
Similar perimeter
Age
14 to 16
Challenge level
What are the possible perimeters of the larger triangle?
problem
Three right angles
Age
14 to 16
Challenge level
Work your way through these right-angled triangles to find $x$.
problem
Doubly isosceles
Age
14 to 16
Challenge level
Find the missing distance in this diagram with two isosceles triangles
problem
Maximum mean
Age
14 to 16
Challenge level
What is the largest that the mean of these numbers could be?
problem
The power of x
Age
14 to 16
Challenge level
Find the value of $x$ in this equation, where it appears in powers.
problem
Winding vine
Age
14 to 16
Challenge level
A vine is growing up a pole. Can you find its length?
problem
Odd dice
Age
14 to 16
Challenge level
These strange dice are rolled. What is the probability that the sum obtained is an odd number?
problem
Square to a rectangle
Age
14 to 16
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?
problem
Inches and barleycorns
Age
14 to 16
Challenge level
How many barleycorns are there in one inch?
problem
Photocopied map
Age
14 to 16
Challenge level
What will the scale on this map be after it has been photocopied?
problem
How many squares?
Age
14 to 16
Challenge level
How many 4-digit numbers are perfect squares?
problem
Semicircle distance
Age
14 to 16
Challenge level
Can you find the shortest distance between the semicircles given the area between them?
problem
Arc radius
Age
14 to 16
Challenge level
Two arcs are drawn in a right-angled triangle as shown. What is the length $r$?
problem
Rotation and area
Age
14 to 16
Challenge level
Point A is rotated to point B. Can you find the area of the triangle that these points make with the origin?
problem
Square in a circle in a square
Age
14 to 16
Challenge level
What is the ratio of the areas of the squares in the diagram?
problem
Root estimation
Age
14 to 16
Challenge level
Which of these is the best approximation for this square root?
problem
Climbing ropes
Age
14 to 16
Challenge level
Given how much this 50 m rope weighs, can you find how much a 100 m rope weighs, if the thickness is different?
problem
Cones and spheres
Age
14 to 16
Challenge level
A solid metal cone is melted down and turned into spheres. How many spheres can be made?