Explaining, convincing and proving
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problemFavouriteSame Length
Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?
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problemFavouriteMarbles in a Box
How many winning lines can you make in a three-dimensional version of noughts and crosses?
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problemFavouriteTake Three From Five
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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problemFavouriteTourism
If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.
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problemFavouriteProduct Sudoku
The clues for this Sudoku are the product of the numbers in adjacent squares.
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problemFavouriteTriangle in a Trapezium
Can you find and prove the relationship between the area of a trapezium and the area of a triangle constructed within it?
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problemFavouritePythagoras Proofs
Can you make sense of these three proofs of Pythagoras' Theorem?
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problemFavouriteShopping Basket
The items in the shopping basket add and multiply to give the same amount. What could their prices be?