Conjecturing and generalising
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gameJam
Age14 to 16Challenge level
To avoid losing think of another very well known game where the patterns of play are similar.
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problemPolycircles
Age14 to 16Challenge level
Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?
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problemA tilted square
Age14 to 16Challenge level
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
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problemHarmonic triangle
Age14 to 16Challenge level
Can you see how to build a harmonic triangle? Can you work out the next two rows?
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problemMixing more paints
Age14 to 16Challenge level
Can you find an efficent way to mix paints in any ratio?
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problemParabolic patterns
Age14 to 18Challenge level
The illustration shows the graphs of fifteen functions. Two of them have equations $y=x^2$ and $y=-(x-4)^2$. Find the equations of all the other graphs.
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problemVector walk
Age14 to 18Challenge level
Starting with two basic vector steps, which destinations can you reach on a vector walk?
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problemDifference dynamics
Age14 to 18Challenge level
Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?