Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

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?

How can you quickly sort a suit of cards in order from Ace to King?

Can you set the logic gates so that this machine can decide how many bulbs have been switched on?

Can you crack these very difficult challenge ciphers? How might you systematise the cracking of unknown ciphers?

Weekly Problem 6 - 2008

From this sum of powers, can you find the sum of the indices?

Weekly Problem 27 - 2015

How many triples of points are there in this 4x4 array that lie on a straight line?

Weekly Problem 27 - 2008

In the diagram in the question, how many squares, of any size, are there whose entries add up to an even total?

Weekly Problem 6 - 2014

A maze has nine rooms, with gaps in the walls between them. How many ways are there to travel from X to Y?

Weekly Problem 39 - 2015

In how many different ways can a row of five "on/off" switches be set so that no two adjacent switches are in the "off" position?

Weekly Problem 8 - 2014

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

Weekly Problem 45 - 2015

If Sam is getting married on the 9th of November 2015 aged 30, do you know which year he was born in?

Weekly Problem 17 - 2014

Tweedledum, Tweedledee, Alice and the White Rabbit are having a conversation. How many of the statements they make are true?

Weekly Problem 16 - 2016

How many three digit numbers have the property that the middle digit is the mean of the other two digits?

You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.

Weekly Problem 34 - 2014

Can you work out how many of Pierre, Qadr, Ratna, Sven and Tanya are telling the truth?

Weekly Problem 18 - 2017

Dominic wants to place the six dominoes above in a hexagonal ring. Which of the dominoes could be placed next to the one shown?

Weekly Problem 8 - 2015

How many ways are there of completing the mini-sudoku shown?

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

Weekly Problem 41 - 2013

The teacher has forgotten which pupil won which medal. In how many different ways could he give the medals out to the pupils?

Weekly Problem 12 - 2011

How many numbers do you need to remove to avoid making a perfect square?

Weekly Problem 24 - 2015

In how many ways can you move through the grid to give the digits 2009?

A collection of short Stage 3 and 4 problems on Working Systematically.

Weekly Problem 25 - 2015

How many different phone numbers are there starting with a 3 and with at most two different digits?

The clues for this Sudoku are the product of the numbers in adjacent squares.