Euclid Contest 2023 - Study Guide

2023 Euclid Contest Study Guide

Tip

This contest was written on April 4-5, 2023. Each question is worth 10 marks with a mix of short-answer and full-solution parts. Good luck studying!

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• Problem 1

  Averages and means
• Problem 2

  Coordinate geometry - midpoints, slopes, perpendicular lines
• Problem 3

  Divisors, consecutive integers, arithmetic sequences
• Problem 4

  Rates of work, percent change
• Problem 5

  Quadratic discriminant, sine rule with triangles
• Problem 6

  Areas of regions, lattice geometry
• Problem 7

  Probability, systems of equations with factoring
• Problem 8

  Pythagorean triples, logarithmic equations
• Problem 9

  Combinatorics - full tables around circular seating
• Problem 10

  Floor function sums and number theory proof

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Problem 1

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Problem 2

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Problem 3

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Problem 4

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Problem 5

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Problem 6

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Problem 7

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Problem 8

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Problem 9

This problem is about circular seating arrangements. A round table with chairs (labeled to ) is “full” if no more people can be seated without two people sitting in neighboring chairs.

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Problem 10

This problem involves the floor function , the greatest integer less than or equal to .

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Key Topics Covered