During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?
Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.
Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.
On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?
The pages of my calendar have got mixed up. Can you sort them out?
What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
How long does it take to brush your teeth? Can you find the matching length of time?
On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?
My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?
Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?
Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?
Find out about Magic Squares in this article written for students. Why are they magic?!
Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?
Two sudokus in one. Challenge yourself to make the necessary connections.
This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.
A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?
The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on. . . .
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?
A Sudoku with clues as ratios.
How many different triangles can you make on a circular pegboard that has nine pegs?
When I fold a 0-20 number line, I end up with 'stacks' of numbers on top of each other. These challenges involve varying the length of the number line and investigating the 'stack totals'.
Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?
In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?
There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.
This is a variation of sudoku which contains a set of special clue-numbers. Each set of 4 small digits stands for the numbers in the four cells of the grid adjacent to this set.
The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
An investigation that gives you the opportunity to make and justify predictions.
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?
Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?
Four small numbers give the clue to the contents of the four surrounding cells.
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Number problems at primary level that require careful consideration.
This Sudoku, based on differences. Using the one clue number can you find the solution?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
How many different differences can you make?
A Sudoku with a twist.
This activity investigates how you might make squares and pentominoes from Polydron.
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.
How many triangles can you make on the 3 by 3 pegboard?