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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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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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Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

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

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

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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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This challenge involves calculating the number of candles needed on birthday cakes. It is an opportunity to explore numbers and discover new things.

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

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

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

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

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Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?

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

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Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

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

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

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

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

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

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Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

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Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

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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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If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

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

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

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Different combinations of the weights available allow you to make different totals. Which totals can you make?

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Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

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Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.