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함께 풀고 싶은 문제
나도 수학쌤 문장제 문제를 변형해 문제를 내는 곳입니다.
[문장제 문제&개념응용] 탄지로의 모험 10탄:으아아아아아아아아아!오랜만에 문제(부제목:함풀문 창의퍼즐에 N 소멸)
비우스 2022.04.17 05:47 조회 259
문제 푼 사람 1명
공유하기
페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

탄지로의 귀환!그동안 문제를 안 냈던 이유를 수학동아팀(은 아니고 그냥 기유가)이 인터뷰했다.

기자(기유):그동안 폴매에 문제를 단 1문제도 내지 않으신 이유가 뭡니까?

탄지로:문제는 뫼비우스가 내는데요...

기자(기유):그럼 뫼비우스씨는 어디에.....

탄지로:지금 문제를 개발하고 있습니다.

기자(기유):그런데 시간이 넘 오래 걸리내요.걍 탄지로씨가 문제를 만들어주세요.

그래서 만들어진 게 이 문제다.

1.탄지로와 뫼비우스가 NIM게임을 한다.한번에 돌을 1개부터 9개까지 가져갈 수 있다.(돌을 가져가지 않을 수는 없다.)돌이 총 30001개일 때,누구에게 필승전략이 있을까?(단,뫼비우스가 먼저 시작하고,마지막 돌을 가져가는 사람이 이긴다.)

2.이번에는 한번에 돌을 1개부터 n개까지 가져갈 수 있다.그리고,돌은 총 Z개 있다.뫼비우스가 반드시 이기려면,n과 Z 사이에 어떤 관계가 있어야 할까?(단 뫼비우스가 먼저 시작하고,돌을 1개도 가져가지 않을 순 없다.)

 

 

풀이 필수&두 문제 다 풀어야 해결

이 문제 어떠셨나요?

글쎄요

1

어려워요

0

문제 찜하기 목록보기
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  •  
    다시 도전
    '나' Lv.7 2022.04.17 19:01 비밀댓글
    비밀 댓글이 등록 되었습니다.
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    •  
      비우스 Lv.8 2022.04.18 05:23 비밀댓글
      비밀 댓글이 등록 되었습니다!
  •  
    필즈상 Lv.6 2022.04.17 22:39

    1. 뫼비우스

    풀이: 뫼비우스가 일단 4개를 가져간다. 그 후 탄지로가 t개를 가져가면 뫼비우스는 (10-t)개를 가져가면 뫼비우스가 무조건 이기게 된다.

    2. Z는 (n의 배수+1)

    풀이: 뫼비우스가 처음에 1개를 가져간다. 그 후 탄지로가 x개를 가져가면 뫼비우스는 (n-x)개를 가져가면 뫼비우스가 무조건 이기게 된다.

    댓글 작성하기 좋아요0 댓글수0
  •  
    '나' Lv.7 2022.04.18 06:01 비밀댓글
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  •  
    비우스 Lv.8 2022.04.19 04:56

    본문에 나옵니다.

    댓글 작성하기 좋아요0 댓글수1
    •  
      '나' Lv.7 2022.04.19 04:58

      그렇네요!

      좋아요0
  •  
    해결
    '나' Lv.7 2022.04.19 05:43 비밀댓글
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    •  
      비우스 Lv.8 2022.04.19 05:45

      정답인데 돌은 3001개가 아니고 30001개입니

      다....

      좋아요0
    •  
      '나' Lv.7 2022.04.19 05:47

      오타가 났네요... 죄송합니다....

      좋아요0
  •  
    '나' Lv.7 2022.04.19 05:45 비밀댓글
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  •  
    다시 도전
    jane Lv.8 2022.04.23 19:51 비밀댓글

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    비밀 댓글이 등록 되었습니다.
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    •  
      비우스 Lv.8 2022.04.24 04:53

      근데 1번에서 필승전략은 누구에게 있는 건가요?

      좋아요0
    •  
      jane Lv.8 2022.04.24 06:42

      탄지로요

      좋아요0

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