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?

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

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

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

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

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

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?

Here are some rods that are different colours. How could I make a yellow rod using white and red rods?

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

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

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?

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.

How many trains can you make which are the same length as Matt's and Katie's, using rods that are identical?

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

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?

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?

Number problems at primary level that require careful consideration.

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

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?

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.

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

Use the numbers and symbols to make this number sentence correct. How many different ways can you find?

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

Using the statements, can you work out how many of each type of rabbit there are in these pens?

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

What happens when you try and fit the triomino pieces into these two grids?

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

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

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

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.

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?

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

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

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?

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?

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

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Have a go at this game which has been inspired by the Big Internet Math-Off 2019. Can you gain more columns of lily pads than your opponent?

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

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 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?

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

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

How long does it take to brush your teeth? Can you find the matching length of time?

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