Weekly Problem 38 - 2013

A regular hexagon is divided into six equilateral triangles. How many quadrilaterals are there in the diagram?

Weekly Problem 49 - 2009

What is the smallest number of ferry trips that Neda needs to take to visit all four islands and return to the mainland?

Weekly Problem 8 - 2012

How many routes are there in this diagram from S to T?

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Weekly Problem 16 - 2012

If the odd numbers on two dice are made negative, which of the totals cannot be achieved?

Weekly Problem 32 - 2013

What order did Jack have the cards in to make his card trick work?

Weekly Problem 2 - 2007

How many different flags can you make?

Weekly Problem 33 - 2013

Squares of the type shown are sewn together to make a quilt. How many different quilts can be made?

Weekly Problem 22 - 2007

The Famous Five have been given 20 sweets as a reward for solving a tricky crime.... how many different ways can they share the sweets?

Weekly Problem 26 - 2011

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

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

Can you find a way to identify times tables after they have been shifted up?

Weekly Problem 31 - 2011

Can you find a number and its double using the digits $1$ to $9$ only once each?

Weekly Problem 31 - 2016

The diagram shows a grid of $16$ identical equilateral triangles. How many rhombuses are there made up of two adjacent small triangles?

Weekly Problem 53 - 2011

Find a number between 100 and 999 that has its middle digit equal to the sum of the other two digits. Can you find all possibilities?

Can you picture how to order the cards to reproduce Charlie's card trick for yourself?

Weekly Problem 32 - 2016

What is the smallest integer which has every digit a 3 or a 4 and is divisible by both 3 and 4?

Weekly Problem 29 - 2006

No letter is repeated in any row, column or diagonal. Which letter is in the square marked with the star?

Weekly Problem 35 - 2011

You are given lots of clues about a number. Can you work out what it is?

Weekly Problem 44 - 2016

Two of the four small triangles are to be painted black. In how many ways can this be done?

Weekly Problem 38 - 2006

What is the fewest coins that must change hands if I buy a ticket for 44p?

Weekly Problem 10 - 2009

In how many ways can you give change for a ten pence piece?

Weekly Problem 40 - 2010

Can you remove the least number of points from this diagram, so no three of the remaining points are in a straight line?

Weekly Problem 4 - 2013

On my clock's display, the time has just changed to 02:31. How many minutes will it be until all the digits 0, 1, 2, 3 next appear together again?

Weekly Problem 28 - 2015

Can you choose one number from each row and column in this grid to form the largest possibe product?

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

Weekly Problem 14 - 2013

At how many times between 10 and 11 o'clock are all six digits on a digital clock different?

Weekly Problem 39 - 2006

What is the fewest gloves that Dilly needs to bring Granny to ensure that they have a pair?

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

Weekly Problem 43 - 2010

The squares of this grid contain one of the letters P, Q, R and S. Can you complete this square so that touching squares do not contain the same letter? How many possibilities are there?

Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

Weekly Problem 20 - 2006

How many ways are there to make 11p using 1p, 2p and 5p coins?

Weekly Problem 42 - 2008

How many different ways could we have sat on the two remaining musical chairs at Gill's fourth birthday party?

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

Can you find rectangles where the value of the area is the same as the value of the perimeter?

Weekly Problem 21 - 2011

How many ways can you paint this wall with four different colours?

How many different symmetrical shapes can you make by shading triangles or squares?

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

Weekly Problem 25 - 2016

A list is made of every digit that is the units digit of at least one prime number. How many digits appear in the list?

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?

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 - 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 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?

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.

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

Weekly Problem 27 - 2015

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

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 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 12 - 2011

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

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 45 - 2015

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

Weekly Problem 34 - 2014

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

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 8 - 2015

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

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?