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HMMT 2017 C5

  • Combinatorics
  • Answer

Kelvin the Frog likes numbers whose digits strictly decrease, but numbers that violate this condition in at most one place are good enough. In other words, if did_{i} denotes the ii th digit, then di≤di+1d_{i} \leq d_{i+1} for at most one value of ii. For example, Kelvin likes the numbers 43210, 132, and 3, but not the numbers 1337 and 123. How many 5-digit numbers does Kelvin like?

Dataset text NuminaMath olympiads. Quoted with source.

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14034

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