Weekly Problem 17 - 2011

Every third page number in this book has been omitted. Can you work out what number will be on the last page?

Weekly Problem 23 - 2011

MatildaMatildaMatil... What is the 1000th letter?

Weekly Problem 40 - 2012

What is the first term of a Fibonacci sequence whose second term is 4 and fifth term is 22?

Weekly Problem 36 - 2010

How many squares are needed to continue this pattern?

Weekly Problem 30 - 2016

The base of a pyramid has n edges. What is the difference between the number of edges of the pyramid and the number of faces?

Weekly Problem 50 - 2011

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

This sequence is given by the mean of the previous two terms. What is the fifth term in the sequence?

Weekly Problem 5 - 2016

How many hexagons are required for the perimeter of the whole shape to have length 1002cm?

Weekly Problem 27 - 2010

This pattern repeats every 12 dots. Can you work out what a later piece will be?

Weekly Problem 6 - 2016

Luis writes down seven consecutive positive integers. The sum of the three smallest numbers is 33. What is the sum of the three largest numbers?

Weekly Problem 42 - 2012

What number appears immediately below 400 in the triangle?

Weekly Problem 46 - 2011

Multiply a sequence of n terms together. Can you work out when this product is equal to an integer?

Weekly Problem 52 - 2010

Leonard writes down a sequence of numbers. Can you find a formula to predict the seventh number in his sequence?

Weekly Problem 24 - 2017

What is the last digit of $3^{2011}$?

Weekly Problem 8 - 2011

This grocer wants to arrange his fruit in a particular order, can you help him?

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 51 - 2017

How many numbers less than 2017 are both the sum of two consecutive integers and the sum of five consecutive integers?

Counters are placed on an 8 by 8 chessboard... What fraction of the counters are on squares of the same colour as themselves?

Weekly Problem 9 - 2011

Barbara is putting draughts on a $4x4$ board in a particular way. Can you find the least number of draughts she needs to put down?

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?

Grannie's watch gains 30 minutes every hour, whilst Grandpa's watch loses 30 minutes every hour. What is the correct time when their watches next agree?

Weekly Problem 35 - 2014

A sequence is generated using these rules. For which values of n is the nth term equal to n?

Weekly Problem 35 - 2010

Knights always tell the truth. Knaves always lie. Can you catch these knights and knaves out?

Weekly Problem 14 - 2016

In a supermarket, there are two lines of tightly packed trolleys. What is the length of one trolley?

Weekly Problem 44 - 2012

Consider two arithmetic sequences: 1998, 2005, 2012,... and 1996, 2005, 2014,... Which numbers will appear in both?

Weekly Problem 46 - 2012

If a number is even, halve it; if odd, treble it and add 1. If a sequence starts at 13, what will be the value of the 2008th term?

Weekly Problem 41 - 2012

The fifth term of a Fibbonaci sequence is 2004. If all the terms are positive integers, what is the largest possible first term?