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In this game you are challenged to gain more columns of lily pads than your opponent.

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

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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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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Can you work out how to make each side of this balance equally balanced? You can put more than one weight on a hook.

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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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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.?

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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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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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.

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Try this matching game which will help you recognise different ways of saying the same time interval.

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

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My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?

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

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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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Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

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This task follows on from Build it Up and takes the ideas into three dimensions!

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Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

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Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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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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This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

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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?

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

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

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What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

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Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

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

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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?

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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....?

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

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

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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?

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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?

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I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

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

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Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

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

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This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

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Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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

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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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On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

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