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Maximum number of phone numbers in a company

Source: Moldova NMO 2002 grade 8 problem nr.4

November 2, 2008

Problem Statement

All the internal phone numbers in a certain company have four digits. The director wants the phone numbers of the administration offices to consist of digits 1 1, 2 2, 3 3 only, and that any of these phone numbers coincide in at most one position. What is the maximum number of distinct phone numbers that these offices can have ?