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MATH / Six-digit integers will be written using each of the digits 1 through 6 exactly once per six-digit integer. How many different positive integers can be written such that all pairs …

Problem

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problem

Six-digit integers will be written using each of the digits 11 through 66 exactly once per six-digit integer. How many different positive integers can be written such that all pairs of consecutive digits of each integer are relatively prime? (Note: 11 is relatively prime to all integers.)
Plain-text mathematical notation (without MathML)
Six-digit integers will be written using each of the digits 1 through 6 exactly once per six-digit integer. How many different positive integers can be written such that all pairs of consecutive digits of each integer are relatively prime? (Note: 1 is relatively prime to all integers.)
Original LaTeX notation
Six-digit integers will be written using each of the digits $1$ through $6$ exactly once per six-digit integer. How many different positive integers can be written such that all pairs of consecutive digits of each integer are relatively prime? (Note: $1$ is relatively prime to all integers.)

level

Level 5

type

Number Theory

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Source and history

task_id
7e446689-eea2-584b-aa76-58324dc6c6b0
task_key
number~5ftheory--test--7e446689-eea2-584b-aa76-58324dc6c6b0
task_revision_id
1
config / split
number_theory / test

Official source

initial import