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set of 5-digit numbers - All-Russian MO 2004 Regional (R4) 10.6

Source:

September 27, 2024
number theoryDigits

Problem Statement

A set of five-digit numbers {N1,...,Nk}\{N_1, ...,N_k\} is such that any five-digit number, all of whose digits are in non-decreasing order, coincides in at least one digit with at least one of the numbers N1N_1, ...... , NkN_k. Find the smallest possible value of kk.
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