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

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

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

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

Different combinations of the weights available allow you to make different totals. Which totals can you make?

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

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

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

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?

Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

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?

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

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?

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 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?

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

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

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?

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.

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

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

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

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

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?

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.

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

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.

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

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

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?

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

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?

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

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.

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

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?

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

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?

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

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

How will you go about finding all the jigsaw pieces that have one peg and one hole?

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?

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

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