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Print51st 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