# SEAMC Published Shorts

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

### 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?

### Black and White Socks

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

Find the missing distance in this diagram with two isosceles triangles

### Maximum Mean

##### Age 14 to 16 ShortChallenge Level

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

### Thousands of X

##### Age 14 to 16 ShortChallenge Level

Can you solve this scary-looking equation?

### Big Product

##### Age 14 to 16 ShortChallenge Level

How many digits are there in this product?

### Snapped Palm Tree

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

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

### 3-4-5 Circle

##### Age 14 to 16 ShortChallenge Level

Can you find the radius of the circle inscribed inside a '3-4-5 triangle'?

### Square to a Rectangle

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

How many barleycorns are there in one inch?

### Square and Triangle

##### Age 14 to 16 ShortChallenge Level

Can you find the area of the yellow square?

### Order the Products

##### Age 14 to 16 ShortChallenge Level

Can you put these products in order of size?

### The Power of $x$

##### Age 14 to 16 ShortChallenge Level

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

### Odd Dice

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

A solid metal cone is melted down and turned into spheres. How many spheres can be made?

### CD Collection

##### Age 14 to 16 ShortChallenge Level

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

### Rough Root

##### Age 14 to 16 ShortChallenge Level

Which of these options is closest to this square root?

### How Many Squares?

##### Age 14 to 16 ShortChallenge Level

How many 4-digit numbers are perfect squares?

### Slide Height

##### Age 14 to 16 ShortChallenge Level

How high is the top of the slide?

### 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 $2^{48}-1$.

### 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