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수학동아 - 폴리매스
함께 풀고 싶은 문제
창의력을 기를 수 있는 수학 문제 또는 퍼즐을 내는 곳입니다.
[창의 퍼즐] [★★★☆☆] 컴컴한 방과 세 개의 스위치
솔바람
2021.12.18 05:10
조회 397
Peter Winkler의 'The Spinning Switches' 문제를 변형
당신은 칠흑같이 어두운 방에 홀로 갇혔다.
앞을 더듬거리며 주위를 둘러보았더니, 출구는 세 자물쇠에 의해 삼중으로 잠겨 있고
방 한가운데에는 원기둥 위에 세 개의 스위치가 있다는 것을 알게 되었다.
각각의 스위치를 켜고 꺼서 각각의 자물쇠를 열리거나 잠기게 할 수 있다.
그런데 방이 너무나도 어두워 스위치의 켜진 상태와 꺼진 상태를 구분할 수 없다.(그래서 각 스위치의 처음 상태 역시 알 수 없다.)
게다가, 스위치를 동시에 여러 개 혹은 어떤 하나를 눌러 문을 열기를 시도한다면
시도 후 즉시 원기둥이 가운데를 중심으로 몇 바퀴 회전하여 이전에 누른 스위치가 무엇이었는지 알 수 없게 된다.
그렇다면 스위치를 누르는 횟수를 가능한 한 적게 하면서, 최소한의 시도로 탈출을 확신하려면
각각의 시도에서 스위치를 어떻게 눌러야 할까?
*풀이 필수*
-
솔바람
Lv.10
2021.12.18 05:14
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