SEAMC Published Shorts


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


Three Right Angles

Age 14 to 16 Short Challenge Level:

Work your way through these right-angled triangles to find $x$.

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?

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?

Pineapple Juice

Age 14 to 16 Short Challenge Level:

What percentage of this orange drink is juice?

Dolly Dolphin

Age 14 to 16 Short Challenge Level:

Can you find Dolly Dolphin's average speed as she swims with and against the current?

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?

Doubly Isosceles

Age 14 to 16 Short Challenge Level:

Find the missing distance in this diagram with two isosceles triangles

Maximum Mean

Age 14 to 16 Short Challenge Level:

What is the largest that the mean of these numbers could be?

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?

Triangle Radius

Age 14 to 16 Short Challenge Level:

Can you find the radii of the small circles?

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?

Tilted Aquarium

Age 14 to 16 Short Challenge Level:

Can you find the depth of water in this aquarium?

Power of Five

Age 14 to 16 Short Challenge Level:

Powers with brackets, addition and multiplication

Late for Work

Age 14 to 16 Short Challenge Level:

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

Nested Square Roots

Age 14 to 16 Short Challenge Level:

Can you find the value of this expression, which contains infinitely nested square roots?

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?

Changing Averages

Age 14 to 16 Short Challenge Level:

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

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?

Graph Triangles

Age 14 to 16 Short Challenge Level:

Use the information about the triangles on this graph to find the coordinates of the point where they touch.

Two Trains

Age 14 to 16 Short Challenge Level:

Two trains started simultaneously, each travelling towards the other. How long did each train need to complete the journey?

Folded Rectangle

Age 14 to 16 Short Challenge Level:

Can you find the perimeter of the pentagon formed when this rectangle of paper is folded?

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?

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?

Face Order

Age 14 to 16 Short Challenge Level:

How many ways can these five faces be ordered?

Inside a Parabola

Age 14 to 16 Short Challenge Level:

A triangle of area 64 square units is drawn inside the parabola $y=k^2-x^2$. Find the value of $k$.

Power of 3

Age 14 to 16 Short Challenge Level:

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

Third Side

Age 14 to 16 Short Challenge Level:

What are the possible lengths for the third side of this right-angled triangle?

How Many Gorillas?

Age 14 to 16 Short Challenge Level:

If the numbers in this news article have been estimated, then what is the largest number of gorillas that there could have been 10 years ago?

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?

Laps

Age 14 to 16 Short Challenge Level:

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

Find the Factor

Age 14 to 16 Short Challenge Level:

Find a factor of $2^{48}-1$.

Candles

Age 14 to 16 Short Challenge Level:

What is the ratio of the lengths of the candles?

Four Circles

Age 14 to 16 Short Challenge Level:

Can you find the radius of the larger circle in the diagram?

Stolen Pension

Age 14 to 16 Short Challenge Level:

How much money did the pensioner have before being robbed?

Triangular Slope

Age 14 to 16 Short Challenge Level:

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

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?

Great Power

Age 14 to 16 Short Challenge Level:

Which is greater: $10^{250}$ or $6^{300}$?

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 $\frac xy$?

Winning Marble

Age 14 to 16 Short Challenge Level:

How can this prisoner escape?

Dropouts

Age 14 to 16 Short Challenge Level:

What percentage of students who graduate have never been to France?

Fraction of Percentages

Age 14 to 16 Short Challenge Level:

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

Smartphone Screen

Age 14 to 16 Short Challenge Level:

Can you find the length and width of the screen of this smartphone in inches?

Powerful 9

Age 14 to 16 Short Challenge Level:

What is the last digit of this calculation?

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?

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?

Closer to Home

Age 14 to 16 Short Challenge Level:

Which of these lines comes closer to the origin?