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6 votes
2 answers
304 views

Hamiltonian path in bike-lock graph with $1$ known digit

Motivation. My youngest son has a bike lock with dials, and he forgot the unlocking combination completely, except that he remembered that digit $0$ appeared somewhere in the combination. So it was my ...
7 votes
3 answers
2k views

"Gray code" for building teams

Motivation. In a team of $n$ people, we had the task to build subteams of a fixed size $k<n$ such that every day, $1$ person of the subteam is replaced by another person in the team, but not in the ...