A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Cache::$apc is deprecated

Filename: libraries/Driver.php

Line Number: 188

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
Line: 22
Function: driver

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
Line: 17
Function: initiateCache

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Cache::$file is deprecated

Filename: libraries/Driver.php

Line Number: 188

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
Line: 22
Function: driver

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
Line: 17
Function: initiateCache

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents_model::$best_cnt is deprecated

Filename: ver3/Contents_model.php

Line Number: 17

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Contents_model.php
Line: 17
Function: _error_handler

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 440
Function: model

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 29
Function: initMenu

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents_model::$popular_cnt is deprecated

Filename: ver3/Contents_model.php

Line Number: 18

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Contents_model.php
Line: 18
Function: _error_handler

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 440
Function: model

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 29
Function: initMenu

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Cache::$dummy is deprecated

Filename: libraries/Driver.php

Line Number: 188

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Contents_model.php
Line: 799
Function: get

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 605
Function: getComment

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Article_model::$best_cnt is deprecated

Filename: ver3/Article_model.php

Line Number: 18

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Article_model.php
Line: 18
Function: _error_handler

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 322
Function: model

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 392
Function: getFloatingMyInfo

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 559
Function: get_footer

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Article_model::$popular_cnt is deprecated

Filename: ver3/Article_model.php

Line Number: 19

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Article_model.php
Line: 19
Function: _error_handler

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 322
Function: model

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 392
Function: getFloatingMyInfo

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 559
Function: get_footer

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

수학동아 - 폴리매스
본문바로가기
함께 풀고 싶은 문제
창의력을 기를 수 있는 수학 문제 또는 퍼즐을 내는 곳입니다.
[창의 퍼즐] 부활의 수
sincostan 2019.10.01 09:59 조회 536

(1)임의의 세자리 자연수에서 그 자연수로 만들 수 있는 가장 큰수와 가장 작은 수를

만들어서뺀다.이 과정을 8번 반복하였을때 8번 이내에 495가 반드시 존재함을 증명하시오.

(2) (1)과 같은 방법으로 임의의 네자리 자연수를 할때 8번 이내에 6174가 반드시 존재함을

증명하시오.(단,직접 모든 경우의 수를 해봐서 증명하는 것은 정답으로 인정하지 않는다.)

이 문제 어떠셨나요?

글쎄요

0

어려워요

0

  •  
    sincostan Lv.7 2019.10.01 10:01

    반드시 비댓으로 정답을 보내 주시고 풀이과정을 올려주세요.

    댓글 작성하기 좋아요0 댓글수0
  •  
    디듀우 Lv.7 2019.10.02 04:23

    어떤 자연수로 만들 수 있는 수는 자릿수를 바꾸는 것을 말씀하신 건가요?

    댓글 작성하기 좋아요0 댓글수0
  •  
    부분해결
    와우~~~~ Lv.2 2019.10.02 09:05 비밀댓글
    비밀 댓글이 등록 되었습니다.
    댓글 작성하기 댓글수1
    •  
      sincostan Lv.7 2019.10.03 09:33

      정답으로 인정하겠습니다.

      좋아요0
  •  
    수학오리 Lv.4 2019.10.06 22:44 비밀댓글
    확인요청중
    비밀 댓글이 등록 되었습니다.
    댓글 작성하기 댓글수2
    •  
      sincostan Lv.7 2019.10.09 08:54

      아닙니다.

      좋아요0
    •  
      수학오리 Lv.4 2019.10.09 20:59

      1111 이나 1000 등은 안되는 걸로 봐서 문제 조건을 가장 큰 수와 가장 작은수가 2이상 차이난다는 조건 같은게 필요하지 않나요?

      좋아요0
  •  
    수학오리 Lv.4 2019.10.08 07:05 비밀댓글
    비밀 댓글이 등록 되었습니다.
    댓글 작성하기 댓글수0
  • 폴리매스 문제는 과학기술진흥기금 및 복권기금의 재원으로 운영되고, 과학기술정보통신부와 한국과학창의재단의 지원을 받아 수행된 성과물로 우리나라의 과학기술 발전과 사회적 가치 증진에 기여하고 있습니다.

  • ☎문의 02-6749-3911