April 2002, Stage 3&4

Problems

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Farey Sequences

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

There are lots of ideas to explore in these sequences of ordered fractions.

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Great Granddad

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

Great Granddad is very proud of his telegram from the Queen congratulating him on his hundredth birthday and he has friends who are even older than he is... When was he born?

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Basically

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

The number 3723(in base 10) is written as 123 in another base. What is that base?

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Mediant

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

If you take two tests and get a marks out of a maximum b in the first and c marks out of d in the second, does the mediant (a+c)/(b+d)lie between the results for the two tests separately.

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Lens Angle

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

Find the missing angle between the two secants to the circle when the two angles at the centre subtended by the arcs created by the intersections of the secants and the circle are 50 and 120 degrees.