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51st Ukrainian National Mathematical Olympiad, 3rd Round

Ukraine counting and probability

Problem

Find maximal natural even number, with all distinct digits such that the difference between any two consecutive digits is at least 2.
Solution
We start in the same way as in 7-1. We have the first piece . If the next digit is , then the next one is and all even digits are used. So the next digit should be . And we get the answer: .
Final answer
9758641302

Techniques

Games / greedy algorithmsColoring schemes, extremal arguments