Number Operations - October 2005, Stage 4&5

Problems

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Different by One

Stage: 4 Challenge Level: Challenge Level:1

Make a line of green and a line of yellow rods so that the lines differ in length by one (a white rod)

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Stretching Fractions

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

Imagine a strip with a mark somewhere along it. Fold it in the middle so that the bottom reaches back to the top. Stetch it out to match the original length. Now where's the mark?

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Data Chunks

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

Data is sent in chunks of two different sizes - a yellow chunk has 5 characters and a blue chunk has 9 characters. A data slot of size 31 cannot be exactly filled with a combination of yellow and. . . .

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Pythagorean Fibs

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

What have Fibonacci numbers got to do with Pythagorean triples?

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Fibonacci Fashion

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

What have Fibonacci numbers to do with solutions of the quadratic equation x^2 - x - 1 = 0 ?

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Plus or Minus

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Make and prove a conjecture about the value of the product of the Fibonacci numbers $F_{n+1}F_{n-1}$.