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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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Take three consecutive numbers and add them together. What do you notice?

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In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?

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Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?

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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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Try entering different sets of numbers in the number pyramids. How does the total at the top change?

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How much of the square is coloured blue? How will the pattern continue?

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It's easy to work out the areas of most squares that we meet, but what if they were tilted?

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Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

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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 describe this route to infinity? Where will the arrows take you next?

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Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?

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Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...

A collection of short Stage 3 and 4 problems on Reasoning, Justifying, Convincing and Proof.

Challenge Level

Can you find the values at the vertices when you know the values on the edges?

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What can we say about all the primes which are greater than 3?

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There are lots of different methods to find out what the shapes are worth - how many can you find?

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How many sets of three consecutive odd numbers can you find, in which all three numbers are prime?

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Is there a quick and easy way to calculate the sum of the first 100 odd numbers?

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Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?

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How many winning lines can you make in a three-dimensional version of noughts and crosses?

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If you take four consecutive numbers and add them together, the answer will always be even. What else do you notice?

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Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?

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Take four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

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Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

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Can you create a Latin Square from multiples of a six digit number?

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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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Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

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Which numbers cannot be written as the sum of two or more consecutive numbers?

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$40$ can be written as $7^2 - 3^2.$ Which other numbers can be written as the difference of squares of odd numbers?

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Are these statistical statements sometimes, always or never true? Or it is impossible to say?

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Can you match the charts of these functions to the charts of their integrals?

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This group tasks allows you to search for arithmetic progressions in the prime numbers. How many of the challenges will you discover for yourself?

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Explore the properties of some groups such as: The set of all real numbers excluding -1 together with the operation x*y = xy + x + y. Find the identity and the inverse of the element x.

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Which of these triangular jigsaws are impossible to finish?