Given the products of diagonally opposite cells - can you complete this Sudoku?

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

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?

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?

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

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 find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

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 work out which cities Mohamed, Sheng, Tanya and Bharat live in.

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

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

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

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!

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?

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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

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. . . .

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

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.

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

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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?

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

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

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

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

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?

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?

Design an arrangement of display boards in the school hall which fits the requirements of different people.

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

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

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

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

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

A Sudoku that uses transformations as supporting clues.

This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.

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?

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