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51st Ukrainian National Mathematical Olympiad, 3rd Round

Ukraine counting and probability

Problem

Find maximal natural number, with all distinct digits such that the difference between any two consecutive digits is at least .
Solution
It is clear that our number has to have digits. We start with (it is clear that cannot be neither second nor third digit). - are first six digits. We can't have after, so we have , and finally the answer is: .
Final answer
9758642031

Techniques

Games / greedy algorithmsColoring schemes, extremal argumentsAlgorithms