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?
Use cunning to work out a strategy to win this game.
Can you crack these very difficult challenge ciphers? How might you systematise the cracking of unknown ciphers?
Weekly Problem 8 - 2015
How many ways are there of completing the mini-sudoku shown?
A collection of short Stage 3 and 4 problems on Working Systematically.
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 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?
Weekly Problem 32 - 2011
What could be the scores from five throws of this dice?
Weekly Problem 25 - 2015
How many different phone numbers are there starting with a 3 and with at most two different digits?
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 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 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 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 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?
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?