Being curious
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problemBeelines
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
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problemTriangle midpoints
You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?
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problemDoesn't add up
In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?
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problemExpenses
What is the largest number which, when divided into these five numbers in turn, leaves the same remainder each time?
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problemFair shares?
A mother wants to share some money by giving each child in turn a lump sum plus a fraction of the remainder. How can she do this to share the money out equally?
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problemWhat's possible?
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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problemArclets
Each of the following shapes is made from arcs of a circle of radius r. What is the perimeter of a shape with 3, 4, 5 and n "nodes". -
problemPick's theorem
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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problemTriangles and petals
An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?