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How many solutions can you find to this sum? Each of the different letters stands for a different number.

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15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

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Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

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Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

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If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

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Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?

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Can you find rectangles where the value of the area is the same as the value of the perimeter?

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Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

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Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

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How many different symmetrical shapes can you make by shading triangles or squares?

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Can you find a way to identify times tables after they have been shifted up or down?

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A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?

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Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

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Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

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Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

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

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Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

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My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

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Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

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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?

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

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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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Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

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A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

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By selecting digits for an addition grid, what targets can you make?

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A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

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Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

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Each clue in this Sudoku is the product of the two numbers in adjacent cells.

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The clues for this Sudoku are the product of the numbers in adjacent squares.

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Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?

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The items in the shopping basket add and multiply to give the same amount. What could their prices be?

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Use the differences to find the solution to this Sudoku.

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Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

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How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?