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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?

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

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

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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?

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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.

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.

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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?

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

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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?

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Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?

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Can you find out in which order the children are standing in this line?

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

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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?

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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?

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

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.

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

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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?

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.

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Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

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

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

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

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

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My coat has three buttons. How many ways can you find to do up all the buttons?

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

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My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?

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Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.

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

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

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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?

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

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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?

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

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

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

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A challenging activity focusing on finding all possible ways of stacking rods.

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

Number problems for lower primary that will get you thinking.

A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.

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

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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?

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The brown frog and green frog want to swap places without getting wet. They can hop onto a lily pad next to them, or hop over each other. How could they do it?

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Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

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

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In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

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

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