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.

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?

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.

My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?

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.?

In this matching game, you have to decide how long different events take.

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 order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

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....?

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?

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?

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

Find out about Magic Squares in this article written for students. Why are they magic?!

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?

Four small numbers give the clue to the contents of the four surrounding cells.

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

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?

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

How many different triangles can you make on a circular pegboard that has nine pegs?

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 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?

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.

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?

Find out what a "fault-free" rectangle is and try to make some of your own.

An investigation that gives you the opportunity to make and justify predictions.

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?

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?

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?

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

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.

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.

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

Number problems at primary level that require careful consideration.

This Sudoku, based on differences. Using the one clue number can you find the solution?

Can you find all the different ways of lining up these Cuisenaire rods?

Two sudokus in one. Challenge yourself to make the necessary connections.