SEAMC Published Shorts


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


Megabytes and Kilobytes

KS 3 Short Challenge Level:

Challenge Level:1

How many bytes are there in one megabyte?

Identical Digit Multiplication

KS 3 Short Challenge Level:

Challenge Level:1

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

Cuboid Faces

KS 3 Short Challenge Level:

Challenge Level:1

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

Roses and Carnations

KS 3 Short Challenge Level:

Challenge Level:1

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

Choose the Mean

KS 3 Short Challenge Level:

Challenge Level:1

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

Giant Rubik's Cube

KS 3 Short Challenge Level:

Challenge Level:1

How many cubes would be visible in a 12 by 12 by 12 Rubik’s cube?

Hot-dogs

KS 3 Short Challenge Level:

Challenge Level:1

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

Draining a Pool

KS 3 Short Challenge Level:

Challenge Level:1

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

Fraction of a Square

KS 3 Short Challenge Level:

Challenge Level:1

What fraction of this square is shaded?

2014 Even Numbers

KS 3 Short Challenge Level:

Challenge Level:1

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

Adding and Multiplying

KS 3 Short Challenge Level:

Challenge Level:1

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

Speed over a Bridge

KS 3 Short Challenge Level:

Challenge Level:1

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

Overlapping Beer Mats

KS 3 Short Challenge Level:

Challenge Level:1

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

Reverse Ages

KS 3 Short Challenge Level:

Challenge Level:1

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

Bouncing Ball

KS 3 Short Challenge Level:

Challenge Level:1

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.

Split Clock Face

KS 3 Short Challenge Level:

Challenge Level:1

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.

Mean Balance

KS 3 Short Challenge Level:

Challenge Level:1

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

Dance Party

KS 3 Short Challenge Level:

Challenge Level:1

At a party, each man danced with exactly three women, and each woman danced with exactly two men. If 12 men attended the party, how many women attended?

Missing Digits

KS 3 Short Challenge Level:

Challenge Level:1

Can you find the missing digits in this calculation?

Divisible Digits

KS 3 Short Challenge Level:

Challenge Level:1

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

Tile Border

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Palindromic Milometer

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Square Grid

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Tilted Tank

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Shifting Average

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Brothers and Sisters

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Sum of 1s

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Can you find the last 5 digits of this sum?

Multiplication Mistake

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Diagonal Side

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Dividing a Square

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Tiled Floor

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Missing 9s

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Which Face?

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Lattice Points on a Line

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Graph Area

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Charlie's Money

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

How much money did Charlie have to begin with?

Red Card Blue Card

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Inches and Barleycorns

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

How many barleycorns are there in one inch?

Scalene Area

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Can you find the area of this scalene triangle?

Committees

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Cuboid Perimeters

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Packing Small Boxes

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

How many small boxes will fit inside the big box?

Clubs

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Clock Angle

KS 3 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

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

Add All the Angles

KS 3 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

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

Leap Monday

KS 3 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

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

Tricky Fractions

KS 3 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

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

Black and Gold Storeys

KS 3 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

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

Last Digit

KS 3 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

What is the last digit in this calculation involving powers?

Washing Elephants

KS 3 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

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

Rain

KS 3 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

How many dry days did Aisha have on her holiday?

Cones and Spheres

KS 4 Short Challenge Level:

Challenge Level:1

A solid metal cone is melted down and turned into spheres. How many spheres can be made?

Square to a Rectangle

KS 4 Short Challenge Level:

Challenge Level:1

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?

Bobbly Perimeter

KS 4 Short Challenge Level:

Challenge Level:1

Find the perimeter of this shape made of semicircles

Flipping Coins

KS 4 Short Challenge Level:

Challenge Level:1

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

Root 2017

KS 4 Short Challenge Level:

Challenge Level:1

Between which two whole numbers is $\sqrt{2017}$ $?$

Table Total

KS 4 Short Challenge Level:

Challenge Level:1

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

Semicircle Distance

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Can you find the shortest distance between the semicircles given the area between them?

CD Collection

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

How many different ways can I arrange the CDs in my collection?

Power of 3

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

What power of 27 is needed to get the correct power of 3?

Square Overlap

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

The top square has been rotated so that the squares meet at a 60$^\text{o}$ angle. What is the area of the overlap?

Growing Triangle

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

XOXOXO

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Odd Dice

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

These strange dice are rolled. What is the probability that the sum obtained is an odd number?

Square in a Circle in a Square

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Thousands of X

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Can you solve this scary-looking equation?

Traffic Tunnel

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Will these vehicles fit through this tunnel?

Snapped Palm Tree

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Fraction of Percentages

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

What is $W$ as a fraction of $Z?$

3-4-5 Circle

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Swapping Sweets

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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?

Strike a Chord

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Black and White Socks

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Difference Sequence

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

When will 2000 appear in this sequence?

Slide Height

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

How high is the top of the slide?

Pineapple Juice

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

What percentage of this orange drink is juice?

Clever Calculation

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Find the shortcut to do this calculation quickly!

Doubly Isosceles

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Find the missing distance in this diagram with two isosceles triangles

Winding Vine

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

A vine is growing up a pole. Can you find its length?

Diagonal Area

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

A Third of the Area

KS 4 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

The area of the small square is $\frac13$ of the area of the large square. What is $\frac xy$?

Candles

KS 4 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

What is the ratio of the lengths of the candles?

Triangular Intersection

KS 4 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

What is the largest number of intersection points that a triangle and a quadrilateral can have?

Pay Attention

KS 4 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

If some of the audience fell asleep for some of this talk, what was the average proportion of the talk that people heard?

Changing Averages

KS 4 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

Find the value of $m$ from these statements about a group of numbers

Triangular Slope

KS 4 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you find the gradients of the lines that form a triangle?

Boys and Girls

KS 4 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you find the total number of students in the school, given some information about ratios?

Adding a Square to a Cube

KS 4 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

If you take a number and add its square to its cube, how often will you get a perfect square?

Petrol Stop

KS 4 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

From the information given, can you work out how long Roberto drove for after putting petrol in his car?

Laps

KS 4 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

On which of the hare's laps will she first pass the tortoise?

Late for Work

KS 4 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

What average speed should Ms Fanthorpe drive at to arrive at work on time?

Digging Holes

KS 4 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

How long will it take one man and two dogs to dig 15 holes?

The Roller and the Triangle

KS 4 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

How much of the inside of this triangular prism can Clare paint using a cylindrical roller?

Face Order

KS 4 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

How many ways can these five faces be ordered?

Hexagon Perimeter

KS 4 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

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

Overlapping Ribbons

KS 4 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

Two ribbons are laid over each other so that they cross. Can you find the area of the overlap?

Elephants and Geese

KS 4 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

Yesterday, at Ulaanbaatar market, a white elephant cost the same amount as 99 wild geese. How many wild geese cost the same amount as a white elephant today?

Winning Marble

KS 4 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

How can this prisoner escape?