# SEAMC Published Shorts

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

### Missing Digits

##### Age 11 to 14 Short Challenge Level:

Can you find the missing digits in this calculation?

### Range of Averages

##### Age 11 to 14 Short Challenge Level:

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

### Multiplication Cube

##### Age 11 to 14 Short Challenge Level:

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

### 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?

### 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?

### Nested Squares

##### Age 11 to 14 Short Challenge Level:

What proportion of the diagram is shaded?

### 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?

### Sum and Differences

##### Age 11 to 14 Short 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?

### 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?

### 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?

### 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?

### Square Within a Square Within...

##### Age 11 to 14 Short Challenge Level:

What fraction of this square is shaded?

### Fraction of a Square

##### Age 11 to 14 Short Challenge Level:

What fraction of this square is shaded?

### 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?

### 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.

### Strange Dice

##### Age 11 to 14 Short Challenge Level:

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

### 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.

### Rough Rectangle

##### Age 11 to 14 Short Challenge Level:

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

### 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?

### 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.

### Rotation Identification

##### Age 11 to 14 Short Challenge Level:

Which of these can be obtained by rotating this shape?

### Cuboid Faces

##### Age 11 to 14 Short Challenge Level:

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

### Brothers and Sisters

##### Age 11 to 14 Short Challenge Level:

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

##### Age 11 to 14 Short Challenge Level:

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

### 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?

### Product of Fractions

##### Age 11 to 14 Short Challenge Level:

Find the product of these mixed numbers

### Tiled Floor

##### Age 11 to 14 Short Challenge Level:

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

### Clubs

##### Age 11 to 14 Short Challenge Level:

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

### 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?

### 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?

### 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 ?

### Diagonal Side

##### Age 11 to 14 Short Challenge Level:

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

### Smallest Fraction

##### Age 11 to 14 Short Challenge Level:

Which of these is the smallest?

### The Elephant Diet

##### Age 11 to 14 Short Challenge Level:

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

### Shifting Average

##### Age 11 to 14 Short Challenge Level:

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

### Scalene Area

##### Age 11 to 14 Short Challenge Level:

Can you find the area of this scalene triangle?

### Average Temperature

##### Age 11 to 14 Short Challenge Level:

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

### Between a Sixth and a Twelfth

##### Age 11 to 14 Short Challenge Level:

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

### Square Grid

##### Age 11 to 14 Short Challenge Level:

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

### 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?

### Tile Border

##### Age 11 to 14 Short Challenge Level:

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

### 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?

### The Average Age

##### Age 11 to 14 Short Challenge Level:

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

### Roses and Carnations

##### Age 11 to 14 Short Challenge Level:

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

### Charlie's Money

##### Age 11 to 14 Short Challenge Level:

How much money did Charlie have to begin with?

### Linear Area

##### Age 11 to 14 Short Challenge Level:

Find the area of the triangle enclosed by these lines.

### French Test

##### Age 11 to 14 Short Challenge Level:

What was the average score in this French test?

### 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?

### 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?

### Packing Small Boxes

##### Age 11 to 14 Short Challenge Level:

How many small boxes will fit inside the big box?

### 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?

### Number of Arms

##### Age 11 to 14 Short Challenge Level:

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

### Sum of 1s

##### Age 11 to 14 Short Challenge Level:

Can you find the last 5 digits of this sum?

### 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?

### Clock Angle

##### Age 11 to 14 Short Challenge Level:

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

### 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?

### 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...

### Divisible by 55

##### Age 11 to 14 Short Challenge Level:

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

### Tricky Fractions

##### Age 11 to 14 Short Challenge Level:

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

##### Age 11 to 14 Short Challenge Level:

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

### Rain

##### Age 11 to 14 Short Challenge Level:

How many dry days did Aisha have on her holiday?

##### Age 11 to 14 Short Challenge Level:

What fraction of this triangle is shaded?

### Ratio of Areas

##### Age 14 to 16 Short Challenge Level:

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

### Megabytes and Kilobytes

##### Age 14 to 16 Short Challenge Level:

How many bytes are there in one megabyte?

### Cat on a Wall

##### Age 14 to 16 Short Challenge Level:

How high is the wall that this cat is lying on?

### 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?

### Length, Width and Area

##### Age 14 to 16 Short Challenge Level:

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

### Power up to 1000

##### Age 14 to 16 Short Challenge Level:

Find $x+y$, where $2^x\times5^y=1000$

### 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?

### The Power of the Sum

##### Age 14 to 16 Short Challenge Level:

What is this sum, expressed as a power of 2?

### Which Face?

##### Age 14 to 16 Short Challenge Level:

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

### Mean Balance

##### Age 14 to 16 Short Challenge Level:

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

### 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?

### Stacked Cubes

##### Age 14 to 16 Short Challenge Level:

What is the total surface area of this shape?

### Bobbly Perimeter

##### Age 14 to 16 Short Challenge Level:

Find the perimeter of this shape made of semicircles

### Thousands of X

##### Age 14 to 16 Short Challenge Level:

Can you solve this scary-looking equation?

### Big Product

##### Age 14 to 16 Short Challenge Level:

How many digits are there in this product?

### 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?

### 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?

### Photocopied Map

##### Age 14 to 16 Short Challenge Level:

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

### 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'?

### 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?

### Inches and Barleycorns

##### Age 14 to 16 Short Challenge Level:

How many barleycorns are there in one inch?

### Square and Triangle

##### Age 14 to 16 Short Challenge Level:

Can you find the area of the yellow square?

### Order the Products

##### Age 14 to 16 Short Challenge Level:

Can you put these products in order of size?

### The Power of $x$

##### Age 14 to 16 Short Challenge Level:

Find the value of $x$ in this equation, where it appears in powers.

### 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?

### 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?

### CD Collection

##### Age 14 to 16 Short Challenge Level:

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

### Rough Root

##### Age 14 to 16 Short Challenge Level:

Which of these options is closest to this square root?

### How Many Squares?

##### Age 14 to 16 Short Challenge Level:

How many 4-digit numbers are perfect squares?

### Slide Height

##### Age 14 to 16 Short Challenge Level:

How high is the top of the slide?

### Difference Sequence

##### Age 14 to 16 Short Challenge Level:

When will 2000 appear in this sequence?

##### Age 14 to 16 Short Challenge Level:

Two arcs are drawn in a right-angled triangle as shown. What is the length $r$?

### Rotation and Area

##### Age 14 to 16 Short Challenge Level:

Point A is rotated to point B. Can you find the area of the triangle that these points make with the origin?

### Climbing Ropes

##### Age 14 to 16 Short 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?