SEAMC Published Shorts


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


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?

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?

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?

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.

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.

Mean Balance

Age 11 to 14 Short Challenge Level:

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

Dance Party

Age 11 to 14 Short Challenge Level:

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

Age 11 to 14 Short Challenge Level:

Can you find the missing digits in this calculation?

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?

Megabytes and Kilobytes

Age 11 to 14 Short Challenge Level:

How many bytes are there in one megabyte?

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?

Cuboid Faces

Age 11 to 14 Short Challenge Level:

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

Roses and Carnations

Age 11 to 14 Short Challenge Level:

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

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.

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?

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?

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?

Fraction of a Square

Age 11 to 14 Short Challenge Level:

What fraction of this square is shaded?

Diagonal Side

Age 11 to 14 Short Challenge Level:

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

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?

Tiled Floor

Age 11 to 14 Short Challenge Level:

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

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?

Which Face?

Age 11 to 14 Short Challenge Level:

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

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 ?

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?

Charlie's Money

Age 11 to 14 Short Challenge Level:

How much money did Charlie have to begin with?

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?

Inches and Barleycorns

Age 11 to 14 Short Challenge Level:

How many barleycorns are there in one inch?

Scalene Area

Age 11 to 14 Short Challenge Level:

Can you find the area of this scalene triangle?

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?

Cuboid Perimeters

Age 11 to 14 Short Challenge Level:

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

Packing Small Boxes

Age 11 to 14 Short Challenge Level:

How many small boxes will fit inside the big box?

Clubs

Age 11 to 14 Short Challenge Level:

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

Tile Border

Age 11 to 14 Short Challenge Level:

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

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?

Square Grid

Age 11 to 14 Short Challenge Level:

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

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?

Shifting Average

Age 11 to 14 Short Challenge Level:

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

Brothers and Sisters

Age 11 to 14 Short Challenge Level:

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

Sum of 1s

Age 11 to 14 Short Challenge Level:

Can you find the last 5 digits of this sum?

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?

Last Digit

Age 11 to 14 Short Challenge Level:

What is the last digit in this calculation involving powers?

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?

Rain

Age 11 to 14 Short Challenge Level:

How many dry days did Aisha have on her holiday?

Clock Angle

Age 11 to 14 Short Challenge Level:

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

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

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?

Tricky Fractions

Age 11 to 14 Short Challenge Level:

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

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...

Root 2017

Age 14 to 16 Short Challenge Level:

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

Table Total

Age 14 to 16 Short Challenge Level:

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

Cones and Spheres

Age 14 to 16 Short Challenge Level:

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

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?

Bobbly Perimeter

Age 14 to 16 Short Challenge Level:

Find the perimeter of this shape made of semicircles

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?

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?

Difference Sequence

Age 14 to 16 Short Challenge Level:

When will 2000 appear in this sequence?

Slide Height

Age 14 to 16 Short Challenge Level:

How high is the top of the slide?

Pineapple Juice

Age 14 to 16 Short Challenge Level:

What percentage of this orange drink is juice?

Clever Calculation

Age 14 to 16 Short Challenge Level:

Find the shortcut to do this calculation quickly!

Doubly Isosceles

Age 14 to 16 Short Challenge Level:

Find the missing distance in this diagram with two isosceles triangles

Winding Vine

Age 14 to 16 Short Challenge Level:

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

Diagonal Area

Age 14 to 16 Short Challenge Level:

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

Semicircle Distance

Age 14 to 16 Short Challenge Level:

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

CD Collection

Age 14 to 16 Short Challenge Level:

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

Power of 3

Age 14 to 16 Short Challenge Level:

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

Square Overlap

Age 14 to 16 Short Challenge Level:

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

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?

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?

Odd Dice

Age 14 to 16 Short Challenge Level:

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

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?

Thousands of X

Age 14 to 16 Short Challenge Level:

Can you solve this scary-looking equation?

Traffic Tunnel

Age 14 to 16 Short Challenge Level:

Will these vehicles fit through this tunnel?

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?

Fraction of Percentages

Age 14 to 16 Short Challenge Level:

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

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'?

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?

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?

Adding a Square to a Cube

Age 14 to 16 Short Challenge Level:

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

Petrol Stop

Age 14 to 16 Short Challenge Level:

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

Laps

Age 14 to 16 Short Challenge Level:

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

Late for Work

Age 14 to 16 Short Challenge Level:

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

Digging Holes

Age 14 to 16 Short Challenge Level:

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

The Roller and the Triangle

Age 14 to 16 Short Challenge Level:

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

Face Order

Age 14 to 16 Short Challenge Level:

How many ways can these five faces be ordered?

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?

Overlapping Ribbons

Age 14 to 16 Short Challenge Level:

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

Elephants and Geese

Age 14 to 16 Short Challenge Level:

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

Age 14 to 16 Short Challenge Level:

How can this prisoner escape?

A Third of the Area

Age 14 to 16 Short Challenge Level:

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

Candles

Age 14 to 16 Short Challenge Level:

What is the ratio of the lengths of the candles?

Triangular Intersection

Age 14 to 16 Short Challenge Level:

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

Pay Attention

Age 14 to 16 Short Challenge Level:

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

Age 14 to 16 Short Challenge Level:

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

Triangular Slope

Age 14 to 16 Short Challenge Level:

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

Boys and Girls

Age 14 to 16 Short Challenge Level:

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