Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

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

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

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?

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

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

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

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

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

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.

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?

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

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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

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

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

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

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.

What is the smallest number of coins needed to make up 12 dollars and 83 cents?

How many possible necklaces can you find? And how do you know you've found them all?

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....?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

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

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.

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

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

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?

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

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

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

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

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.

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?

What is the best way to shunt these carriages so that each train can continue its journey?

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

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

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

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

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

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

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

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

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?

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

You have 5 darts and your target score is 44. How many different ways could you score 44?