# 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?

### 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?

##### 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?