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수학동아 - 폴리매스
함께 풀고 싶은 문제
창의력을 기를 수 있는 수학 문제 또는 퍼즐을 내는 곳입니다.
△π
2020.10.25 13:02
조회 435
4*4 정사각형 판에 1*1 정사각형 15개가 있고, 맨 오른쪽 아래에 공백이 있다. 각각의 정사각형에는 1부터 15까지의 수가 일렬로 써있다.
(1)이 퍼즐의 어떤 모양이던지, n번 움직이면 원래 배열로 돌아올 수 있다. n의 최솟값을 구하시오.(즉, 15퍼즐의 신의 수를 구하시오)
(2)이 퍼즐을 유한번 움직여서 만들 수 있는 모양은 모두 몇 개인지 구하시오(단, 공백의 위치가 다르게 있는 배열 또한 다른 배열로 본다.)
-
1번은 잘 모르겠는데 2번의 답은 다음과 같습니다.
공백 또한 생각해야하므로 공백을 16이라 가정하면
(n이 있던 칸을(n)이라 표시하겠습니다.)
(1)에는 16가지가 가능하고,
(2)에는 (1)의 무언가를 빼고 생각해야하므로15가지,
.
.
.
(15)에는 2가지
(16)에는 1가지가 되고,
이는 16*15*14*13*12*...*3*2*1=16!
입니다.
-
△π
Lv.9
2020.12.09 17:09
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