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수학동아 - 폴리매스
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함께 풀고 싶은 문제
창의력을 기를 수 있는 수학 문제 또는 퍼즐을 내는 곳입니다.
[창의 퍼즐] 평균채우기
MathlabJ 2020.04.10 22:24 조회 915
문제 푼 사람 1명
공유하기
페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

mn개의 단위정사각형 칸으로 이루어진 m×n 직사각형이 있다.(m, n은 2이상)

 

단위정사각형마다 자연수를 집어넣는데, 한 단위정사각형 칸에 있는 수는 그 칸과 이웃한(상하좌우) 칸들에 적힌 수들의 평균이 되도록 하려고 한다.

 

직사각형의 크기가 가장 작게 하려면 어떻게 수를 집어넣야 하며, 몇칸이 필요할까?

 

단, 단위정사각형 칸들에 넣는 수들은 중복이 가능하다.

 

풀이 필수입니다.

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