Problems
Leap Frog
Stage:1 Challenge Level:
The brown frog and green frog want to swap places without getting wet. They can hop onto a lily pad next to them, or hop over each other. How could they do it?
Eight Sticks
Stage:1 Challenge Level:
You have eight sticks. Four of them are half the length of the other four. Lay out all the eight sticks to form three squares of equal size. There can be no loose ends sticking out!
Street Party
Stage:2 Challenge Level:
The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.
1 to 8
Stage:2 Challenge Level:
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
Brothers and Sisters
Stage:2 Challenge Level:
Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?
Clock Face
Stage:2 Challenge Level:
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
Let's Face It
Stage:2 Challenge Level:
In this problem you have to place four by four magic squares on the faces of a cube so that along each edge of the cube the numbers match.
I'm Eight
Stage:1, 2, 3 and 4 Challenge Level:
Find a great variety of ways of asking questions which make 8.
Track
Stage:3 Challenge Level:
The school running track has six lanes, each a metre wide. How far forward should the runner in the outside lane start if the runners are to complete a one lap race fairly?
Cube Paths
Stage:3 Challenge Level:
Given a 2 by 2 by 2 skeletal cube with one route `down' the cube. How many routes are there from A to B?
Right Time
Stage:3 Challenge Level:
At the time of writing the hour and minute hands of my clock are at right angles. How long will it be before they are at right angles again?
Friday 13th
Stage:3 Challenge Level:
This month there is a Friday the thirteenth and this year there are three. Can you explain why every year must contain at least one Friday the thirteenth?
Factorial
Stage:4 Challenge Level:
How many zeros are there at the end of the number which is the product of first hundred positive integers?
Pentakite
Stage:4 and 5 Challenge Level:
ABCDE is a regular pentagon of side length one unit. BC produced meets ED produced at F. Show that triangle CDF is congruent to triangle EDB. Find the length of BE.
How Many Balls?
Stage:5 Challenge Level:
A bag contains red and blue balls. You are told the probabilities of drawing certain combinations of balls. Find how many red and how many blue balls there are in the bag.
Eyes Down
Stage:5 Challenge Level:
The symbol [ ] means 'the integer part of'. Can the numbers [2x]; 2[x]; [x + 1/2] + [x - 1/2] ever be equal? Can they ever take three different values?
Thebault's Theorem
Stage:5 Challenge Level:
Take any parallelogram and draw squares on the sides of the parallelogram. What can you prove about the quadrilateral formed by joining the centres of these squares?
