The problems in this collection have been adapted from problems that have been set in South East Asian Mathematics Competitions.
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
Reverse ages
When is the next time that Brian's age will be the reverse of his father's age?
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
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
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
Divisible digits
Can you find the missing digits, given that the number is divisible by 3, 4, 5 and 6?
problem
Multiplication cube
The net shown is folded up to form a cube. What is the largest possible vertex product?
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
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
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
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
Washing elephants
How long will it take Mary and Nigel to wash an elephant if they work together?
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
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?
problem
Semicircle distance
Can you find the shortest distance between the semicircles given the area between them?
problem
Rotation and area
Point A is rotated to point B. Can you find the area of the triangle that these points make with the origin?
problem
Square in a circle in a square
What is the ratio of the areas of the squares in the diagram?
problem
Climbing ropes
Given how much this 50 m rope weighs, can you find how much a 100 m rope weighs, if the thickness is different?
problem
Cones and spheres
A solid metal cone is melted down and turned into spheres. How many spheres can be made?