Upper Secondary - Complete Article Index

Take a few whole numbers away from a triangle number. If you know the mean of the remaining numbers can you find the triangle number and which numbers were removed?

Anna, Bridget and Carol run a race. Can you work out where Carol was when Anna finished?

Here's a neat trick you can do with an 11 by 11 square...

Repeat a pattern of numbers to form a larger number. Can you find the sum of all the digits?

A 2-digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?

Weekly Problem 10 - 2014
What is the sum of the first $2011$ digits when $20 \div 11$ is written as a decimal?

Two circles of equal size intersect and the centre of each circle is on the circumference of the other. What is the area of the intersection? Now imagine that the diagram represents two spheres of equal volume with the centre of each sphere on the surface of the other. What is the volume of intersection?

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

How many triangles can Jack draw with two sides of lengths $6$cm and $8$cm and an area of $7$cm$^2$?

The four digits 5, 6, 7 and 8 are put at random in the spaces of the number : 3 _ 1 _ 4 _ 0 _ 9 2 Calculate the probability that the answer will be a multiple of 396.

Some treasure has been hidden in a three-dimensional grid! Can you work out a strategy to find it as efficiently as possible?

Can you use the clues to complete these 5 by 5 Mathematical Sudokus?

Can you use the clues to complete these 6 by 6 Mathematical Sudokus?

This problem in geometry has been solved in no less than EIGHT ways by a pair of students. How would you solve it? How many of their solutions can you follow? How are they the same or different? Which do you like best?

Find the smallest positive integer N such that N/2 is a perfect cube, N/3 is a perfect fifth power and N/5 is a perfect seventh power.

In this problem, we define complex numbers and invite you to explore what happens when you add and multiply them.

Complex numbers can be represented graphically using an Argand diagram. This problem explains more...

Weekly Problem 43 - 2015
Rachel and Ross share a bottle of water. Can you work out how much water Rachel drinks?

Can you draw a sketch of how Frosty's volume changes as his height decreases?

Here are a collection of statements to prove, to help you to practise writing out clear mathematical proofs.

Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?

What is the mean of this set of numbers?

A geographical survey: answer the tiny questionnaire and then analyse all the collected responses...

What happens when you find the powers of this matrix?

Investigate constructible images which contain rational areas.

A design is repeated endlessly along a line - rather like a stream of paper coming off a roll. Make a strip that matches itself after rotation, or after reflection

First cipher

The Earth is further from the Sun than Venus, but how much further? Twice as far? Ten times?

Find the area of the shaded region created by the two overlapping triangles in terms of a and b?

Can you use the given image to say something about the sum of an infinite series?

What do we REALLY mean when we talk about a tangent to a curve?

The area of the small square is $\frac13$ of the area of the large square. What is $\frac xy$?

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?

This problem explores the biology behind Rudolph's glowing red nose, and introduces the real life phenomena of bacterial quorum sensing.

The mean number of students has changed, so how many students applied to a school?

How many integers $n$ are there for which $n$ and $n^3+3$ are both prime?

If you take a number and add its square to its cube, how often will you get a perfect square?

Is there a quick and easy way to calculate the sum of the first 100 odd numbers?

Can you use Proof by Induction to establish what will happen when you add more and more odd numbers?

Find four integers whose sum is 400 and such that the first integer is equal to twice the second integer, three times the third integer and four times the fourth integer.

In a 7-digit numerical code, each group of four consecutive digits adds to 16, and each group of five consecutive digits adds to 19. What is the sum of all 7 digits?

Observe symmetries and engage the power of substitution to solve complicated equations.

How do you choose your planting levels to minimise the total loss at harvest time?

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

Alberta won't reveal her age. Can you work it out from these clues?

The mean of three numbers x, y and z is x. What is the mean of y and z?

If $6x-y=21$ and $6y-x=14$, what is the value of $x-y$?

The planet Zog has both green and blue bank notes. Can you work out how many zogs two green and three blue bank notes are worth?

Can you tangle yourself up and reach any fraction?

The challenge is to find the values of the variables if you are to solve this Sudoku.

If all the arrangements of the letters in the word ANGLE are written down in alphabetical order, what position does the word ANGLE occupy?

This Sudoku requires you to do some working backwards before working forwards.

Given that the number 2008 is the correct answer to a sum, can you find n?

In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.

Weekly Problem 8 - 2010
Are you able to find triangles such that these five statements are true?

Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.

Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.

Can you use the diagram to prove the AM-GM inequality?

Three of Santa's elves and their best friends are sitting down to a festive feast. Can you find the probability that each elf sits next to their bestie?