SEAMC Published Shorts


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


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?

Arc Radius

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 βˆšπ‘› 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?

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?

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?