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.?

Can you find the chosen number from the grid using the clues?

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

What could the half time scores have been in these Olympic hockey matches?

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

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

Can you order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

Moira is late for school. What is the shortest route she can take from the school gates to the entrance?

When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

My coat has three buttons. How many ways can you find to do up all the buttons?

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there be?

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?

These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

Can you use this information to work out Charlie's house number?

Can you find out in which order the children are standing in this line?

How many trapeziums, of various sizes, are hidden in this picture?

The Zargoes use almost the same alphabet as English. What does this birthday message say?

Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

Put 10 counters in a row. Find a way to arrange the counters into five pairs, evenly spaced in a row, in just 5 moves, using the rules.

My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way to share the sweets between the three children so they each get the kind they like. Is there more than one way to do it?

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

Investigate the different ways you could split up these rooms so that you have double the number.

Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

Using the statements, can you work out how many of each type of rabbit there are in these pens?

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?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

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.

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?