this month, Stage 3 & 4

May 2002

 

Problems

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Teddy Town

Stage:1, 2 and 3 Challenge Level:Challenge Level:2Challenge Level:2

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

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Going Loopy

Stage:3 Challenge Level:Challenge Level:1

Spiralling out of control! I should have known better. Merely mentioning the word spiral and suggestions and reminders abound. Below are some spirals done by pupils at a recent Masterclass at the. . . .

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Powerful Factorial

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

6! = 6 x 5 x 4 x 3 x 2 x 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4 ) = 45. What is the highest power of two that divides exactly into 100!?

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Domino Tetrads

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

Is it possible to use all 28 dominoes arranging them in squares of four? What patterns can you see in the solution(s)?

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Similarly So

Stage:4 Challenge Level:Challenge Level:3Challenge Level:3Challenge Level:3

ABCD is a square. P is the midpoint of AB and is joined to C. A line from D perpendicular to PC meets the line at the point Q. Prove AQ = AD.

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Approximating Pi

Stage:4 Challenge Level:Challenge Level:3Challenge Level:3Challenge Level:3

By inscribing a circle in a square and then a square in a circle find an approximation to pi. By using a hexagon, can you improve on the approximation?