# SEAMC Published Shorts

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

##### Age 14 to 16 ShortChallenge Level

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

### Rotation and Area

##### Age 14 to 16 ShortChallenge 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 ShortChallenge 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 ShortChallenge Level

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

### Two in a Million

##### Age 14 to 16 ShortChallenge Level

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

### Winding Vine

##### Age 14 to 16 ShortChallenge Level

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

### Cube Factors

##### Age 14 to 16 ShortChallenge Level

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

### Roots Near 9

##### Age 14 to 16 ShortChallenge Level

For how many integers ð‘› is the difference between âˆšð‘› and 9 is less than 1?

### Clever Calculation

##### Age 14 to 16 ShortChallenge Level

Find the shortcut to do this calculation quickly!

### Coal Truck

##### Age 14 to 16 ShortChallenge Level

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

### Similar Perimeter

##### Age 14 to 16 ShortChallenge Level

What are the possible perimeters of the larger triangle?

### Semicircle Distance

##### Age 14 to 16 ShortChallenge Level

Can you find the shortest distance between the semicircles given the area between them?

### Root Estimation

##### Age 14 to 16 ShortChallenge Level

Which of these is the best approximation for this square root?

### Traffic Tunnel

##### Age 14 to 16 ShortChallenge Level

Will these vehicles fit through this tunnel?

### Powerful Expressions

##### Age 14 to 16 ShortChallenge Level

Put these expressions in order, from smallest to largest.

### Growing Triangle

##### Age 14 to 16 ShortChallenge Level

If the base and height of a triangle are increased by different percentages, what happens to its area?

### XOXOXO

##### Age 14 to 16 ShortChallenge Level

6 tiles are placed in a row. What is the probability that no two adjacent tiles have the same letter on them?

### Diagonal Area

##### Age 14 to 16 ShortChallenge Level

A square has area 72 cm$^2$. Find the length of its diagonal.

### Three Right Angles

##### Age 14 to 16 ShortChallenge Level

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

### Square in a Circle in a Square

##### Age 14 to 16 ShortChallenge Level

What is the ratio of the areas of the squares in the diagram?

### Strike a Chord

##### Age 14 to 16 ShortChallenge Level

Can you work out the radius of a circle from some information about a chord?

### Pineapple Juice

##### Age 14 to 16 ShortChallenge Level

What percentage of this orange drink is juice?

### Dolly Dolphin

##### Age 14 to 16 ShortChallenge Level

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

### Candles

##### Age 14 to 16 ShortChallenge Level

What is the ratio of the lengths of the candles?

### Four Circles

##### Age 14 to 16 ShortChallenge Level

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

### Stolen Pension

##### Age 14 to 16 ShortChallenge Level

How much money did the pensioner have before being robbed?

### Triangular Slope

##### Age 14 to 16 ShortChallenge Level

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

### Petrol Stop

##### Age 14 to 16 ShortChallenge 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 ShortChallenge Level

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

### A Third of the Area

##### Age 14 to 16 ShortChallenge 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 ShortChallenge Level

How can this prisoner escape?

### Dropouts

##### Age 14 to 16 ShortChallenge Level

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

### Fraction of Percentages

##### Age 14 to 16 ShortChallenge Level

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

### Smartphone Screen

##### Age 14 to 16 ShortChallenge Level

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

### Powerful 9

##### Age 14 to 16 ShortChallenge Level

What is the last digit of this calculation?

### Adding a Square to a Cube

##### Age 14 to 16 ShortChallenge 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 ShortChallenge 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 ShortChallenge Level

Which of these lines comes closer to the origin?

##### Age 14 to 16 ShortChallenge Level

Can you find the radii of the small circles?

### Pay Attention

##### Age 14 to 16 ShortChallenge 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 ShortChallenge Level

Can you find the depth of water in this aquarium?

### Power of Five

##### Age 14 to 16 ShortChallenge Level

Powers with brackets, addition and multiplication

### Late for Work

##### Age 14 to 16 ShortChallenge Level

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

### Nested Square Roots

##### Age 14 to 16 ShortChallenge Level

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

### Triangular Intersection

##### Age 14 to 16 ShortChallenge Level

What is the largest number of intersection points that a triangle and a quadrilateral can have?

### Changing Averages

##### Age 14 to 16 ShortChallenge Level

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

### The Roller and the Triangle

##### Age 14 to 16 ShortChallenge Level

How much of the inside of this triangular prism can Clare paint using a cylindrical roller?

### Graph Triangles

##### Age 14 to 16 ShortChallenge 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 ShortChallenge 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 ShortChallenge Level

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

### Overlapping Ribbons

##### Age 14 to 16 ShortChallenge 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 ShortChallenge Level

Can you find the total number of students in the school, given some information about ratios?

### Face Order

##### Age 14 to 16 ShortChallenge Level

How many ways can these five faces be ordered?

### Inside a Parabola

##### Age 14 to 16 ShortChallenge 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 ShortChallenge Level

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

### Third Side

##### Age 14 to 16 ShortChallenge Level

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

### How Many Gorillas?

##### Age 14 to 16 ShortChallenge 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 ShortChallenge 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 ShortChallenge Level

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

### Find the Factor

##### Age 14 to 16 ShortChallenge Level

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