회원가입 | IDPW찾기

페이스북 로그인

전체알림
* 알림은 최근 일주일 내역만 보여집니다.

2020-10-27 00:14:32

풀이라고 생각되는 사진 올린분 공개적으로 엿먹이기

문제 출처 2018 IMO 4번

검색해서 풀이 가져오세요 아무나 ㅋㅋ

댓글[9]

등록하기

사진 등록하기

  • The maximal K is 100. Amy can reach at least 100 by playing only on sites for which x+y is even. There are 200 such sites, none are of distance $\sqrt{5}$ from each other and Ben can occupy at most half of them. On the other hand Ben can prevent Amy from reaching more than 100 using the following strategy: Picture the sites as a 20 by 20 board and divide it into 25 non overlapping 4-by-4 squares. We label each site in the square as follows:\[1, 2, 3, 4\]\[5, 6, 7, 8\]\[8, 7, 6, 5\]\[4, 3, 2, 1\]
    Whenever Amy plays in a square Ben plays in the same square and in the site with the same label. In each square Amy can place at most 2 stones in sites labeled 1,4,6,7 (no three sites with labels from this set are free from distance $\sqrt{5}$ and Amy can play one stone on each label since Ben plays the other). Likewise for the sites labeled 2,3,5,8. So in total Amy can place at most 4 stones in each of the 25 squares for a total of 100 stones.

    2020-10-27 00:29:28

  • 에트왈 3개 개꿀

    2020-10-27 00:29:41

  • .

    2020-10-27 00:16:32

  • 이건가

    2020-10-27 00:15:57

  • 그냥콴다 쳐봣는데있었어요 ㅋㅋ

    2020-10-27 00:15:29

  • 왜있어요 *발

    2020-10-27 00:16:13

  • 어 뭔..

    2020-10-27 00:16:25

  • 전 고대로퍼옴

    2020-10-27 00:16:15

  • ㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋ

    2020-10-27 00:17:04

오늘 하루 보지 않기
닫기