수학동아 - 폴리매스

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함께 풀고 싶은 문제

창의력을 기를 수 있는 수학 문제 또는 퍼즐을 내는 곳입니다.

[창의 퍼즐] [수리]파이파이

cho317jun 2021.03.22 07:01 조회 422

문제 푼 사람 0명

페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

1. '수학을 담은 파이'라는 제과점에서는 파이데이 기념으로 '파이파이(pipie)'라는 메뉴가 신출시되었다.

파이파이에는 초대형 블루베리가 3개, 대형 블루베리가 1개, 중형 블루베리가 4개, 소형 블루베리가 1가, 초소형 블루베리가 5개가 있다.

또 그 뒤를 이어서 초대형 체리가 9개, 대형 체리가 2개, ..., 이렇게 초소형 체리까지 원주율의 값을 이어나간다.

블루베리와 체리가 정확한 구형일 때, 사이즈가 한 단계 감소할 때 마다(초대형=>대형=>중형...) 지름은 원래 크기의 $\frac{7}{8}$ 이 된다.

초대형 체리는 지름이 3.2cm, 중형 블루베리는 지름이 1.8375cm일 때 이 파이에 올려진 모든 열매의 지름은 몇 mm일까?

2. 이때 파이에 올려진 모든 열매의 지름의 합이 자연수가 되려면 초소형 체리와 초소형 블루베리는 각각 몇 mm가 되어야 할까?

2번의 경우 불가능하다면 그 이유도 같이 써 주세요. 풀이는 필수이고, 문제에서 오류를 찾으시면 문의 부탁드립니다 :)

이전글 4. 스도쿠 퍼즐

다음글 [정수]우박수 변형

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