this month, Stage 3 & 4

October 2000

 

Problems

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1 Step 2 Step

Stage:3 Challenge Level:Challenge Level:1

Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. For example: He could go down 1 step, then one step, then 2 steps, then 2, 2, 1, 1, 1, 1. In. . . .

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Eleven

Stage:3 Challenge Level:Challenge Level:2Challenge Level:2

Replace each letter with a digit to make this addition correct.

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Triominoes

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

A triomino is a flat L shape made from 3 square tiles. A chess board is marked into squares the same size as the tiles and just one square, anywhere on the board, is coloured red. Can you cover the. . . .

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Factoring Factorials

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

Find the highest power of 11 that will divide into 1000! exactly.

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LOGO Challenge - Triangles-squares-stars

Stage:3 and 4 Challenge Level:Challenge Level:2Challenge Level:2

Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.

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Natural Sum

Stage:4 Challenge Level:Challenge Level:1

The picture illustrates the sum 1 + 2 + 3 + 4 = (4 x 5)/2. Prove the general formula for the sum of the first n natural numbers and the formula for the sum of the cubes of the first n natural. . . .

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Gift of Gems

Stage:4 Challenge Level:Challenge Level:1

Four jewellers possessing respectively eight rubies, ten saphires, a hundred pearls and five diamonds, presented, each from his own stock, one apiece to the rest in token of regard; and they. . . .

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Beelines

Stage:4 Challenge Level:Challenge Level:1

A straight line joins the points (0,0) and (p,q) on a grid. How many squares does this line cross and why?

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Circle Angles

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

You are given a variable point C inside a circle and any two chords PCS and QCR through C. Investigate the angle RCS.

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Comparing Continued Fractions

Stage:4 and 5 Challenge Level:Challenge Level:2Challenge Level:2

Which of these continued fractions is bigger and why?