SEAMC Published Shorts

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

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?

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?

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?

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?

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?

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?

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

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?

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?

Cuboid Perimeters

Age 14 to 16 Short Challenge Level:

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

Two in a Million

Age 14 to 16 Short Challenge Level:

What is the highest power of 2 that divides exactly into 1000000?

Winding Vine

Age 14 to 16 Short Challenge Level:

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

Cube Factors

Age 14 to 16 Short Challenge Level:

How many factors of $9^9$ are perfect cubes?

Roots Near 9

Age 14 to 16 Short Challenge Level:

For how many integers 𝑛 is the difference between √𝑛 and 9 is less than 1?

Clever Calculation

Age 14 to 16 Short Challenge Level:

Find the shortcut to do this calculation quickly!

Coal Truck

Age 14 to 16 Short Challenge Level:

What percentage of the truck's final mass is coal?

Similar Perimeter

Age 14 to 16 Short Challenge Level:

What are the possible perimeters of the larger triangle?