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IMSO 2021 Mathematics - International Essay Question 2

IMSO Maths · IMSO 2021 Mathematics - International Essay

Question 2

Place each of the numbers 2, 3, 4, 5, 6, 7 and 8 exactly once in the eight empty circles (the position of 1 is already fixed) such that the sum of each pair of adjacent numbers is a prime number. Diagrams are considered the same if one can be obtained from the other by reflection or rotation. List all possible diagrams.

Question illustration

Source wording note: “eight empty circles” is printed in the original. The diagram actually has eight circles in total, with seven empty circles and a fixed 1. The task is interpreted as filling those seven empty circles. The original blank answer diagrams are retained below.

Question illustration