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MathNet 2015-part-01 — 191 problems (EN–VI) Question 165

Math Olympiad Vault · MathNet 2015-part-01 — 191 problems (EN–VI)

Question 165

A decorator will place flowers at eight points around a square flower arrangement, as shown in the figure below. He wants to do this so that, on each side of the arrangement, people always see the same number of flowers. In the example below, there are 11 flowers in total and on each of the 4 sides of the square exactly 4 of them are seen.

a) What is the maximum number of flowers that can be used, considering that on each side of the square exactly 9 flowers must be seen?

b) What is the minimum number of flowers that can be used, considering that on each side of the square exactly 12 flowers must be seen?

Question illustration