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2015 CHMMC Tiebreaker 3 - 3-digit pair cycles

Source:

March 1, 2024

number theoryCHMMC

Problem Statement

Define an

n

-digit pair cycle to be a number with

n^2 + 1

digits between

1

and

n

with every possible pair of consecutive digits. For instance,

11221

is a 2-digit pair cycle since it contains the consecutive digits

11

12

22

, and

21

. How many

3

-digit pair cycles exist?