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

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

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?

The clues for this Sudoku are the product of the numbers in adjacent squares.

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

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?

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?

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?

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

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

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

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

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

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

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?

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?

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

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

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

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

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

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.

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?

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?

Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?

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.

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

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

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?

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?

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

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

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.

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

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?

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

The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.

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?

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 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?

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