Conjecturing and generalising
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problemIn this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest? -
problemNumber differences
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
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problemMore numbers in the ring
If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?
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problemRing a ring of numbers
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
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problemCarrying cards
These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?
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problemCyclic triangles
Make and prove a conjecture about the cyclic quadrilateral inscribed in a circle of radius r that has the maximum perimeter and the maximum area. -
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problemStars
Can you work out what step size to take to ensure you visit all the dots on the circle?
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problemSquare it
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
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problemHundred square
A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?