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

problem

### Overlapping beer mats

Can you find the area of the overlap when these two beer mats are placed on top of each other?

problem

### Identical digit multiplication

77 is multiplied by another two-digit number with identical digits. What is the product?

problem

### Multiplication Cube

The net shown is folded up to form a cube. What is the largest possible vertex product?

problem

### Divisible digits

Can you find the missing digits, given that the number is divisible by 3, 4, 5 and 6?

problem

### 2014 even numbers

What is the difference between the sum of the first 2014 odd numbers and the sum of the first 2014 even numbers?

problem

### Sum and differences

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?

problem

### Draining a pool

The water is being drained from a pool. After how long will the depth of the pool be 144 cm?

problem

### Reverse ages

When is the next time that Brian's age will be the reverse of his father's age?

problem

### Adding and multiplying

Amy misread a question and got an incorrect answer. What should the answer have be?

problem

### Bouncing ball

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.

problem

### Split clock face

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.

problem

### Strange dice

If two of these unusually numbered dice are thrown, how many different sums are possible?

problem

### Multiplication Mistake

Jane accidentally multiplied by 54 instead of 45, and her answer was 198 too big. What number did she multiply 54 by?

problem

### Missing 9s

Sara makes a list of the whole numbers that do not contain any 9s. What is the 300th number on her list?

problem

### Red card blue card

Can you arrange the red and blue cards so that the rules are all followed?

problem

### Roses and Carnations

How many different bunches of flowers can this class buy for their teacher?

problem

### Adding in Pairs

These are the results when 3 numbers were added in pairs. What were the numbers?

problem

### The elephant diet

Use the relationship between the elephant and the rabbit to find out how many carrots the rabbit eats in a day

problem

### Lattice points on a line

How many lattice points are there in the first quadrant that lie on the line 3x + 4y = 59 ?

problem

### Average temperature

The average temperature of six cities is 5$^\circ$C. What is the average temperature when two cities are added?

problem

### between a sixth and a twelfth

The space on a number line between a sixth and a twelfth is split into 3 equal parts. Find the number indicated.

problem

### Palindromic milometer

At the beginning and end of Alan's journey, his milometer showed a palindromic number. Can you find his maximum possible average speed?

problem

### Dividing a square

A square is divided into three shapes which all have equal areas. Can you find the length of this side?

problem

### Washing elephants

How long will it take Mary and Nigel to wash an elephant if they work together?

problem

### Committees

Every member of the club is a member of two committees. How many members are there in the club?

problem

### Black and gold storeys

25 of the storeys of a 50 storey building are painted gold, and the rest are painted black...

problem

### Number of arms

What is the probability that the next person you meet has an above average number of arms?

problem

### Flipping coins

A coin is flipped 4 times. What is the probability of getting heads at least 3 times?

problem

### Swapping Sweets

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?

problem

### Snapped Palm Tree

A palm tree has snapped in a storm. What is the height of the piece that is still standing?

problem

### Hexagon Perimeter

A circle of radius 1 is inscribed in a regular hexagon. What is the perimeter of the hexagon?

problem

### XOXOXO

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

problem

### Black and white socks

There are 20 black socks and some white socks in a drawer. Can you work out how many of the socks are white?

problem

### Odd Dice

These strange dice are rolled. What is the probability that the sum obtained is an odd number?

problem

### Square to a rectangle

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?