A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_URI::$config is deprecated
Filename: core/URI.php
Line Number: 101
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_Router::$uri is deprecated
Filename: core/Router.php
Line Number: 127
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$benchmark is deprecated
Filename: core/Controller.php
Line Number: 75
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$hooks is deprecated
Filename: core/Controller.php
Line Number: 75
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$config is deprecated
Filename: core/Controller.php
Line Number: 75
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$log is deprecated
Filename: core/Controller.php
Line Number: 75
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$utf8 is deprecated
Filename: core/Controller.php
Line Number: 75
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$uri is deprecated
Filename: core/Controller.php
Line Number: 75
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$exceptions is deprecated
Filename: core/Controller.php
Line Number: 75
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$router is deprecated
Filename: core/Controller.php
Line Number: 75
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$output is deprecated
Filename: core/Controller.php
Line Number: 75
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$security is deprecated
Filename: core/Controller.php
Line Number: 75
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$input is deprecated
Filename: core/Controller.php
Line Number: 75
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$lang is deprecated
Filename: core/Controller.php
Line Number: 75
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$load is deprecated
Filename: core/Controller.php
Line Number: 78
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_Cache::$apc is deprecated
Filename: libraries/Driver.php
Line Number: 188
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_Cache::$file is deprecated
Filename: libraries/Driver.php
Line Number: 188
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$cache is deprecated
Filename: core/Loader.php
Line Number: 1279
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$cacher is deprecated
Filename: core/Loader.php
Line Number: 1279
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$jscript is deprecated
Filename: core/Loader.php
Line Number: 1279
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Return type of CI_Session_files_driver::open($save_path, $name) should either be compatible with SessionHandlerInterface::open(string $path, string $name): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice
Filename: drivers/Session_files_driver.php
Line Number: 132
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Return type of CI_Session_files_driver::close() should either be compatible with SessionHandlerInterface::close(): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice
Filename: drivers/Session_files_driver.php
Line Number: 290
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Return type of CI_Session_files_driver::read($session_id) should either be compatible with SessionHandlerInterface::read(string $id): string|false, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice
Filename: drivers/Session_files_driver.php
Line Number: 164
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Return type of CI_Session_files_driver::write($session_id, $session_data) should either be compatible with SessionHandlerInterface::write(string $id, string $data): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice
Filename: drivers/Session_files_driver.php
Line Number: 233
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Return type of CI_Session_files_driver::destroy($session_id) should either be compatible with SessionHandlerInterface::destroy(string $id): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice
Filename: drivers/Session_files_driver.php
Line Number: 313
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Return type of CI_Session_files_driver::gc($maxlifetime) should either be compatible with SessionHandlerInterface::gc(int $max_lifetime): int|false, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice
Filename: drivers/Session_files_driver.php
Line Number: 354
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: Warning
Message: ini_set(): Session ini settings cannot be changed after headers have already been sent
Filename: Session/Session.php
Line Number: 284
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: Warning
Message: session_set_cookie_params(): Session cookie parameters cannot be changed after headers have already been sent
Filename: Session/Session.php
Line Number: 291
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: Warning
Message: ini_set(): Session ini settings cannot be changed after headers have already been sent
Filename: Session/Session.php
Line Number: 306
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: Warning
Message: ini_set(): Session ini settings cannot be changed after headers have already been sent
Filename: Session/Session.php
Line Number: 316
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: Warning
Message: ini_set(): Session ini settings cannot be changed after headers have already been sent
Filename: Session/Session.php
Line Number: 317
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: Warning
Message: ini_set(): Session ini settings cannot be changed after headers have already been sent
Filename: Session/Session.php
Line Number: 318
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: Warning
Message: ini_set(): Session ini settings cannot be changed after headers have already been sent
Filename: Session/Session.php
Line Number: 319
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: Warning
Message: ini_set(): Session ini settings cannot be changed after headers have already been sent
Filename: Session/Session.php
Line Number: 377
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: Warning
Message: ini_set(): Session ini settings cannot be changed after headers have already been sent
Filename: drivers/Session_files_driver.php
Line Number: 108
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: Warning
Message: session_set_save_handler(): Session save handler cannot be changed after headers have already been sent
Filename: Session/Session.php
Line Number: 110
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: Warning
Message: session_start(): Session cannot be started after headers have already been sent
Filename: Session/Session.php
Line Number: 143
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$session is deprecated
Filename: core/Loader.php
Line Number: 1279
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$agent is deprecated
Filename: core/Loader.php
Line Number: 1279
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$contentsStatus is deprecated
Filename: libraries/Common.php
Line Number: 64
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$articleStatus is deprecated
Filename: libraries/Common.php
Line Number: 71
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$db is deprecated
Filename: core/Loader.php
Line Number: 390
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Contents_model.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_DB_mysqli_driver::$failover is deprecated
Filename: database/DB_driver.php
Line Number: 371
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Contents_model.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents_model::$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
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents_model::$popular_cnt is deprecated
Filename: ver3/Contents_model.php
Line Number: 18
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Contents_model.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$member_model is deprecated
Filename: core/Loader.php
Line Number: 353
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Contents_model.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$contents_model is deprecated
Filename: core/Loader.php
Line Number: 353
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$menuList is deprecated
Filename: libraries/Common.php
Line Number: 561
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$common is deprecated
Filename: core/Loader.php
Line Number: 1279
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$dto is deprecated
Filename: core/Loader.php
Line Number: 1279
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Contents::$together_end_date is deprecated
Filename: ver3/Contents.php
Line Number: 17
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_Cache::$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
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_Loader::$benchmark is deprecated
Filename: core/Loader.php
Line Number: 925
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_Loader::$hooks is deprecated
Filename: core/Loader.php
Line Number: 925
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_Loader::$config is deprecated
Filename: core/Loader.php
Line Number: 925
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_Loader::$log is deprecated
Filename: core/Loader.php
Line Number: 925
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_Loader::$utf8 is deprecated
Filename: core/Loader.php
Line Number: 925
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_Loader::$uri is deprecated
Filename: core/Loader.php
Line Number: 925
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
A PHP Error was encountered
Severity: 8192
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수학동아 - 폴리매스
[킹앤카&킹앤포&킹앤유] [포10] 마르쿠스 미니 운동
수학동아 2020.09.29 02:33
조회 941
*KPP 게시판에 잘못 올라가서 새로 올라온 글입니다. 기존 게시판에 댓글 남겨주셨던 space님의 답안은 그대로 응모되었으며 댓글로 달아두겠습니다.
[킹앤포 10월호]
안녕하세요 수학동아입니다.
POSTECH 마르쿠스가 직접 출제하는 퀴즈킹앤포스텍 문제를 풀어보세요!
퀴즈에 참여해주신 분 중 추첨을 통해 선물을 드립니다.
한 문제만 풀어도 좋으니 여러분의 풀이를 보여주세요!
정답이 아닌 기발한 오답도 대환영입니다. 정답이 없으면 기발한 오답을 제출한 분께 선물을 드려요!
킹앤포 문제 풀이에 참여하고 싶은 분은
이 게시물의 비밀댓글로 이름, 연락처, 주소와 함께 풀이를 남겨주세요 ^^
QUIZ 1)
미니 운동회 결과 윤재가 1등, 탁일이 2등, 종호가 3등, 태형이 4등을 했다. 회장 동준은 네 사람에게 선물 상자 네 개를 보여주면서, 이 중 하나에는 상금 10만 원이, 다른 세 개에는 기념 머그컵이 있다고 말했다. 윤재부터 등수 순서대로 선물을 고를 수 있으며, 모두 선물을 받으면 회장은 머그컵을 고른 사람들의 선물을 하나씩 개봉한다. 선물이 하나씩 개봉될 때마다 남은 사람들 중 순위가 가장 높은 사람은 다른 한 명과 선물 교환을 할 수 있다. 윤재가 상금을 획득하기 위해 할 수 있는 최선의 전략은 무엇인가?
QUIZ 2)
쉬는 시간 동안 다같이 점심을 먹는다. 참가한 사람은 총 41명이며 그 중에서 신입부원은 25명, 기존 회원은 16명이다. 테이블은 총 11개고 한 테이블에 최대 4명이 앉을 수 있다. 회장은 다음 조건에 따라 밥 먹을 팀을 정하라고 지시했다.
a. 한 테이블에 최소 세 명은 앉아야 한다. b. 기존 회원이 신입부원보다 많은 테이블은 없어야 한다. c. 모든 테이블을 활용해야 한다.
그렇다면 인원 배치는 어떻게 해야 할까?
수리논술문제)
식사 후 종이컵에 물을 마시던 윤재는 순간 힘을 잘못 주는 바람에 오목해진 종이컵 밖으로 물이 넘치고 말았다. 윤재는 같은 둘레를 가진 종이컵이라도 오목한 모양보다 원 모양컵의 단면적이 더 넓다는 사실에 흥미를 느껴 다음 문제를 생각해냈다. 평면에서 같은 둘레를 가진 도형 중에서 오목한 모양의 도형이 넓이가 가장 크지 않다는 사실을 증명하라. *힌트: 도형이 볼록하다는 것은 그 도형에서 임의의 두 점을 잡을 때 두 점을 잇는 선분에 있는 모든 점이 그 도형 위에 있다는 뜻이다. 오목하다는 것은 볼록하다는 조건을 만족하지 않는 것으로, 별 모양이나 초승달 모양이 오목한 도형이다.
-----------------------------------------------------------------------------------------------------------------------------------------------------
분량 문제로 수학동에 싣지 못한 퀴즈 1번 문제의 답을 공개합니다!
답을 보고싶지 않으시다면 스크롤을 멈추세요!
나머지 문제의 답은 수학동아 2020년 11월호에서 확인할 수 있습니다!
퀴즈 1 의 답은 ' 첫 라운드에서는 교환 , 그 다음 라운드에서는 유지하는 것 ' 입니다 .
윤재가 처음에 바로 탈락하는 경우는 전략의 의미가 없으므로 고려하지 않는다 . 윤재가 처음에 선택되지 않았다면 윤재에게는 두 가지 선택권이 있다 . 만약 윤재가 그대로 유지한다면 윤재는 처음부터 상금을 선택해야 하므로 윤재가 상금을 선택할 확률은 1/4이다 . 만약 윤재가 교환을 시도한다면 윤재가 처음에 머그컵을 골라야 하고 남아있는 두 사람 중 한 명이 상금을 가지고 있으므로 윤재가 상금을 선택할 확률은 3/4 × 1/2 = 3/8이다 .
여기서 윤재가 탈락할 확률은 윤재가 위의 전략에 따랐을 때 머그컵을 고를 확률의 절반이다 . 따라서 윤재가 교환 전략을 사용했다면 5/8 × 1/2 = 5/16이고 , 유지했다면 3/4 × 1/2 = 3/8이다 . 그 다음 라운드에서도 윤재에게는 두 가지 전략이 있다 . 여기서도 그대로 유지한다면 윤재는 전 라운드의 전략에 의해 상금을 선택했어야 한다 . 만약 교환을 시도한다면 전 라운드에서 윤재가 머그컵을 골랐어야 한다 . 정리하면 아래와 같다 .
교환 -교환 전략으로 상금을 얻을 사건의 확률 : 5/16
교환 -유지 전략으로 상금을 얻을 사건의 확률 : 3/8
첫 라운드의 교환 전략으로 탈락할 확률 : 5/16
유지 -교환 전략으로 상금을 얻을 사건의 확률 : 3/8
유지 -유지 전략으로 상금을 얻을 사건의 확률 : 1/4
첫 라운드의 유지 전략으로 탈락할 확률 : 3/8
따라서 , 첫 라운드에서는 교환 , 그 다음 라운드에서는 유지하는 것이 가장 좋은 전략이다 .
박현선
Lv.2 2020.09.29 02:35
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박현선
Lv.2 2020.09.29 02:35
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박현선
Lv.2 2020.09.29 02:36
KPP 게시판에 올라갔을 때 달렸던 Space 님의 댓글입니다
좋아요 0
space
Lv.8 2020.09.29 23:21
좋아요 0
다마츠요
Lv.4 2020.10.08 04:03
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카이스트
Lv.1 2020.10.15 20:49
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