Skip to main content
### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# SEAMC Published Shorts

### Choose the Mean

### Rough Rectangle

### 2014 Even Numbers

### Split Clock Face

### Rotation Identification

### Cuboid Faces

### Brothers and Sisters

### Missing Digits

### Range of Averages

### Multiplication Cube

### Draining a Pool

### Speed over a Bridge

### Overlapping Beer Mats

### Reverse Ages

### Sum and Differences

### Giant Rubik's Cube

### Identical Digit Multiplication

### Adding and Multiplying

### Hot Dogs

### Square Within a Square Within...

### Divisible Digits

### Bouncing Ball

### Strange Dice

### Tile Border

### Dividing a Square

### The Average Age

### Roses and Carnations

### Linear Area

### Tilted Tank

### Graph Area

### Packing Small Boxes

### Adding in Pairs

### Multiplication Mistake

### Tiled Floor

### Clubs

### Palindromic Milometer

### Missing 9s

### Lattice Points on a Line

### Diagonal Side

### The Elephant Diet

### Shifting Average

### Average Temperature

### Between a Sixth and a Twelfth

### Square Grid

### Red Card Blue Card

### Add All the Angles

### Leap Monday

### Number of Arms

### Committees

### Clock Angle

### Last Digit

### Washing Elephants

### Black and Gold Storeys

### Divisible by 55

### Tricky Fractions

### Which Face?

### Mean Balance

### Flipping Coins

### Bobbly Perimeter

### Ratio of Areas

### Swapping Sweets

### Length, Width and Area

### Table Total

### Powerful Expressions

### Growing Triangle

### XOXOXO

### Diagonal Area

### Three Right Angles

### Square in a Circle in a Square

### Strike a Chord

### Dolly Dolphin

### Black and White Socks

### Doubly Isosceles

### Maximum Mean

### Snapped Palm Tree

### Hexagon Perimeter

### Photocopied Map

### 3-4-5 Circle

### Square to a Rectangle

### Inches and Barleycorns

Or search by topic

The problems in this collection have been adapted from problems that have been set in South East Asian Mathematics Competitions.

Age 11 to 14

ShortChallenge Level

Find 4 numbers which have a mean of 7, a median of 8 and a mode of 9.

Age 11 to 14

ShortChallenge Level

What is the smallest possible area that this rectangle could have?

Age 11 to 14

ShortChallenge Level

What is the difference between the sum of the first 2014 odd numbers and the sum of the first 2014 even numbers?

Age 11 to 14

ShortChallenge 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.

Age 11 to 14

ShortChallenge Level

Which of these can be obtained by rotating this shape?

Age 11 to 14

ShortChallenge Level

Can you find the volume of a cuboid, given the areas of its faces?

Age 11 to 14

ShortChallenge Level

Can you work out how many brothers and sisters are in the family?

Age 11 to 14

ShortChallenge Level

Can you find the missing digits in this calculation?

Age 11 to 14

ShortChallenge Level

Find these 4 numbers, given their mode, median and range.

Age 11 to 14

ShortChallenge Level

The net shown is folded up to form a cube. What is the largest possible vertex product?

Age 11 to 14

ShortChallenge Level

The water is being drained from a pool. After how long will the depth of the pool be 144 cm?

Age 11 to 14

ShortChallenge Level

How fast is the train travelling as it goes over the bridge?

Age 11 to 14

ShortChallenge Level

Can you find the area of the overlap when these two beer mats are placed on top of each other?

Age 11 to 14

ShortChallenge Level

When is the next time that Brian's age will be the reverse of his father's age?

Age 11 to 14

ShortChallenge 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?

Age 11 to 14

ShortChallenge Level

How many cubes would be visible in a 12 by 12 by 12 Rubikâ€™s cube?

Age 11 to 14

ShortChallenge Level

77 is multiplied by another two-digit number with identical digits. What is the product?

Age 11 to 14

ShortChallenge Level

Amy misread a question and got an incorrect answer. What should the answer have be?

Age 11 to 14

ShortChallenge Level

How many hot dogs did this hot dog lover eat on the first day of her binge?

Age 11 to 14

ShortChallenge Level

What fraction of this square is shaded?

Age 11 to 14

ShortChallenge Level

Can you find the missing digits, given that the number is divisible by 3, 4, 5 and 6?

Age 11 to 14

ShortChallenge 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.

Age 11 to 14

ShortChallenge Level

If two of these unusually numbered dice are thrown, how many different sums are possible?

Age 11 to 14

ShortChallenge Level

What is the largest possible number of yellow tiles in this pattern?

Age 11 to 14

ShortChallenge Level

A square is divided into three shapes which all have equal areas. Can you find the length of this side?

Age 11 to 14

ShortChallenge Level

Given this information about averages, find the ages of these teachers.

Age 11 to 14

ShortChallenge Level

How many different bunches of flowers can this class buy for their teacher?

Age 11 to 14

ShortChallenge Level

Find the area of the triangle enclosed by these lines.

Age 11 to 14

ShortChallenge Level

Can you find the height of the water in this tilted tank when it is flat?

Age 11 to 14

ShortChallenge Level

Can you find the area between this graph and the x-axis, between x=3 and x=7?

Age 11 to 14

ShortChallenge Level

How many small boxes will fit inside the big box?

Age 11 to 14

ShortChallenge Level

These are the results when 3 numbers were added in pairs. What were the numbers?

Age 11 to 14

ShortChallenge Level

Jane accidentally multiplied by 54 instead of 45, and her answer was 198 too big. What number did she multiply 54 by?

Age 11 to 14

ShortChallenge Level

This tiled floor has 109 purple tiles. How many tiles are there altogether?

Age 11 to 14

ShortChallenge Level

How many students are in the maths club and the science club?

Age 11 to 14

ShortChallenge Level

At the beginning and end of Alan's journey, his milometer showed a palindromic number. Can you find his maximum possible average speed?

Age 11 to 14

ShortChallenge Level

Sara makes a list of the whole numbers that do not contain any 9s. What is the 300th number on her list?

Age 11 to 14

ShortChallenge Level

How many lattice points are there in the first quadrant that lie on the line 3x + 4y = 59 ?

Age 11 to 14

ShortChallenge Level

Can you work out the area of a square drawn on a diagonal?

Age 11 to 14

ShortChallenge Level

Use the relationship between the elephant and the rabbit to find out how many carrots the rabbit eats in a day

Age 11 to 14

ShortChallenge Level

What happens to the average if you subtract 8 from all of the numbers?

Age 11 to 14

ShortChallenge Level

The average temperature of six cities is 5$^\circ$C. What is the average temperature when two cities are added?

Age 11 to 14

ShortChallenge Level

The space on a number line between a sixth and a twelfth is split into 3 equal parts. Find the number indicated.

Age 11 to 14

ShortChallenge Level

Can you work out what fraction of this grid is shaded?

Age 11 to 14

ShortChallenge Level

Can you arrange the red and blue cards so that the rules are all followed?

Age 11 to 14

ShortChallenge Level

Find the sum of all of the angles denoted by letters in this diagram

Age 11 to 14

ShortChallenge Level

Can you find the next time that the 29th of February will fall on a Monday?

Age 11 to 14

ShortChallenge Level

What is the probability that the next person you meet has an above average number of arms?

Age 11 to 14

ShortChallenge Level

Every member of the club is a member of two committees. How many members are there in the club?

Age 11 to 14

ShortChallenge Level

What is the angle between the the hands of a clock at 8:24?

Age 11 to 14

ShortChallenge Level

What is the last digit in this calculation involving powers?

Age 11 to 14

ShortChallenge Level

How long will it take Mary and Nigel to wash an elephant if they work together?

Age 11 to 14

ShortChallenge Level

25 of the storeys of a 50 storey building are painted gold, and the rest are painted black...

Age 11 to 14

ShortChallenge Level

Choose the digits $a$ and $b$ so that this number is divisible by 55.

Age 11 to 14

ShortChallenge Level

Use this series of fractions to find the value of x.

Age 14 to 16

ShortChallenge Level

Which faces are opposite each other when this net is folded into a cube?

Age 14 to 16

ShortChallenge Level

Given information about the mean, can you work out the missing numbers?

Age 14 to 16

ShortChallenge Level

A coin is flipped 4 times. What is the probability of getting heads at least 3 times?

Age 14 to 16

ShortChallenge Level

Find the perimeter of this shape made of semicircles

Age 14 to 16

ShortChallenge Level

What is the ratio of the area of the hexagon to the area of the triangle?

Age 14 to 16

ShortChallenge 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?

Age 14 to 16

ShortChallenge Level

The area of a rectangle is 225 square units. Find its width.

Age 14 to 16

ShortChallenge Level

Can you find the sum of all of the numbers in the table?

Age 14 to 16

ShortChallenge Level

Put these expressions in order, from smallest to largest.

Age 14 to 16

ShortChallenge Level

If the base and height of a triangle are increased by different percentages, what happens to its area?

Age 14 to 16

ShortChallenge Level

6 tiles are placed in a row. What is the probability that no two adjacent tiles have the same letter on them?

Age 14 to 16

ShortChallenge Level

A square has area 72 cm$^2$. Find the length of its diagonal.

Age 14 to 16

ShortChallenge Level

Work your way through these right-angled triangles to find $x$.

Age 14 to 16

ShortChallenge Level

What is the ratio of the areas of the squares in the diagram?

Age 14 to 16

ShortChallenge Level

Can you work out the radius of a circle from some information about a chord?

Age 14 to 16

ShortChallenge Level

Can you find Dolly Dolphin's average speed as she swims with and against the current?

Age 14 to 16

ShortChallenge Level

There are 20 black socks and some white socks in a drawer. Can you work out how many of the socks are white?

Age 14 to 16

ShortChallenge Level

Find the missing distance in this diagram with two isosceles triangles

Age 14 to 16

ShortChallenge Level

What is the largest that the mean of these numbers could be?

Age 14 to 16

ShortChallenge Level

A palm tree has snapped in a storm. What is the height of the piece that is still standing?

Age 14 to 16

ShortChallenge Level

A circle of radius 1 is inscribed in a regular hexagon. What is the perimeter of the hexagon?

Age 14 to 16

ShortChallenge Level

What will the scale on this map be after it has been photocopied?

Age 14 to 16

ShortChallenge Level

Can you find the radius of the circle inscribed inside a '3-4-5 triangle'?

Age 14 to 16

ShortChallenge 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?

Age 14 to 16

ShortChallenge Level

How many barleycorns are there in one inch?