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Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.

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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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During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

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Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

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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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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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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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Two sudokus in one. Challenge yourself to make the necessary connections.

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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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Two sudokus in one. Challenge yourself to make the necessary connections.

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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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Given the products of diagonally opposite cells - can you complete this Sudoku?

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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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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 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?

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

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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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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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Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.

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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?

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In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

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If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

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

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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 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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An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

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

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First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

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In this game for two players, take it in turns to shade one petal, or two petals next to each other. Is it better to go first or second?

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This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?

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How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

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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?

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

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

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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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Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?