Optimum Permutation on a Circle

doi:10.1007/s12045-025-1890-2

Optimum Permutation on a Circle

2025-11-01

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Jyotirmoy Sarkar *

DOI：10.1007/s12045-025-1890-2

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To the vertices of a regular decagon, allocate digits 0 through 9 (using each digit exactly once) so that the product of all ten two-digit numbers in base 10 formed by adjoining each pair of successive digits (always going clockwise) is minimized.What if digits 0,1,& mldr;, (k - 1) are allocated to the vertices of a regular k-gon and the two-digit numbers are read in base k?

Keyword:

Permutation

base k numbers

complete search

number theory

mathematical induction

proof by contradiction

Optimum Permutation on a Circle

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