수학동아 - 폴리매스

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함께 풀고 싶은 문제

깊이 고민해볼 수 있는 수학 문제를 내는 곳입니다

[세상을 바꿀 문제] 크리스마스 기념 문제

아인수타인 2020.12.25 10:01 조회 751

문제 푼 사람 0명

페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

페루마는 크리스마스를 맞이해 크리스마스 트리를 만든다. 이제 거의 다 완성되었고 전구만 달면 된다. 그런데 페루마가 전구를 연결하던 도중, 문득 전구를 다는 방법의 수가 몇 가지인지 궁금해졌다. 예를 들어, 전구가 2개면 직렬로 연결하는 것과 병렬로 연결하는 것 2가지가 있다.

(1) 그러면 페루마가 현재 가지고 있는 전구 4개를 연결하는 방법의 수는?

(2) 전구 $n$ 개를 연결하는 방법의 수를 $a_n$ 이라 할 때, $a_n$ 의 점화식을 구해라. 그리고 일반항도 구해라.

(참고: 아래 그림에서 $A_1$ 과 $A_2, B_1$ 과 $B_2$ 는 같지만, $C_1$ 과 $C_2$ 는 다른 것이다. 즉 연결 상태가 같으면 같은 것이다.)

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code314 Lv.5 2020.12.30 18:36 비밀댓글

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- 아인수타인 Lv.12 2020.12.30 20:47 비밀댓글
  
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아인수타인 Lv.12 2020.12.30 23:54

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