this month, Stage 3 & 4

December 1999

 

Problems

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Sam Again

Stage:3 Challenge Level:Challenge Level:1

Here is a collection of puzzles about Sam's shop sent in by club members. Perhaps you can make up more puzzles, find formulas or find general methods.

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Christmas Boxes

Stage:3 Challenge Level:Challenge Level:1

Find all the ways to cut out a 'net' of six squares that can be folded into a cube.

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As Easy as 1,2,3

Stage:3 Challenge Level:Challenge Level:1

When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type. . . .

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Farmers Field

Stage:3 Challenge Level:Challenge Level:1

A farmer has a flat field and two sons who will each inherit half of the field. The farmer wishes to build a stone wall to divide the field in two so each son inherits the same area. Stone walls are. . . .

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Rolling Triangle

Stage:3 Challenge Level:Challenge Level:3Challenge Level:3Challenge Level:3

The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.

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Special Sums and Products

Stage:3 Challenge Level:Challenge Level:3Challenge Level:3Challenge Level:3

Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.

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LOGO Challenge 10 - Circles

Stage:3 and 4 Challenge Level:Challenge Level:1

In LOGO circles can be described in terms of polygons with an infinite (in this case large number) of sides - investigate this definition further.

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Wrapping Gifts

Stage:4 Challenge Level:Challenge Level:1

A box of size a cm by b cm by c cm is to be wrapped with a square piece of wrapping paper. Without cutting the paper what is the smallest square this can be? Now suppose we want to wrap up a. . . .

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Doodles

Stage:4 Challenge Level:Challenge Level:1

A 'doodle' is a closed intersecting curve drawn without taking pencil from paper. Only two lines cross at each intersection or vertex (never 3), that is the vertex points must be 'double points' not. . . .

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Holly

Stage:4 Challenge Level:Challenge Level:2Challenge Level:2

The ten arcs forming the edges of the "holly leaf" are all arcs of circles of radius 1 cm. Find the length of the perimeter of the holly leaf and the area of its surface.

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Giant Holly Leaf

Stage:4 and 5 Challenge Level:Challenge Level:1

You are asked to find the perimeter and area of a 'holly leaf' Like a real holly leaf, it will not ie flat (it has negative curvature) and what looks like a circle has circumference greater. . . .