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

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

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

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

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?

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?

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

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?

Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?

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

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?

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 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?

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

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

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

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.

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.

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?

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?

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

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.

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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?

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

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

How many trapeziums, of various sizes, are hidden in this picture?

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

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

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

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.

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.

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

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

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

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?

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

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?

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

Number problems for lower primary that will get you thinking.

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

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

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

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

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