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?

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?

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

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

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?

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?

Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?

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?

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

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

These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

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

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

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 task follows on from Build it Up and takes the ideas into three dimensions!

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

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?

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

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

How many different rectangles can you make using this set of rods?

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.

Use these head, body and leg pieces to make Robot Monsters which are different heights.

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.?

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?

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

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

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

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

Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?

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

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

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

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

My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?

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?

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

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

This article for primary teachers suggests ways in which to help children become better at working systematically.

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