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수학동아 - 폴리매스
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[잡담] 도움이 필요해요!
오레오맛 아이스크림 2022.01.05 07:47 조회 468

어제 학원끝나고 slither.io라는 지렁이게임을했습니다. 생각보다 재밌더군요 ㅎ

게임에서는 한 지렁이의 머리와 다른 지렁이의 몸통이 부딪히면 머리가 부딪힌 지렁이가 죽습니다.

게임을 하다가 생각난 문제인데 잘 안풀려서 올립니다....

우선, nxn 모양 칸에 1x2 크기의 지렁이들을 겹치지 않게 배열합니다.

이때, 지렁이의 머리와 꼬리를 각각 칸 1개라고 생각하고, 머리와 머리가 부딪히지 않게(가로 또는 세로로 직접적으로 부딪혀야합니다) 배열하는 방법이 몇가지일까요...?(n은 짝수)

 

꼬리

머리     or   (꼬리 머리) (머리 꼬리)   이렇게 만나야 부딪히는걸로 생각합니다

머리

꼬리

 

생각해본 방법은 여러가지인데

지렁이의 머리를 O, 꼬리를 X라 두고 n*n에 O들끼리 만나지 않게 배열하는 가짓수로 바꿔봤는데 좀처럼 답이 나오지않네요ㅠ

고수분들 도와주세요!

 

 

대충 이렇게요

 

 

+ 돌려서 같은 모양은 하나로 셉니다

  • 폴리매스 문제는 과학기술진흥기금 및 복권기금의 재원으로 운영되고, 과학기술정보통신부와 한국과학창의재단의 지원을 받아 수행된 성과물로 우리나라의 과학기술 발전과 사회적 가치 증진에 기여하고 있습니다.

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