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
주니어 폴리매스 문제
수학 문제를 푸는 매력에 빠져 보세요!
[KPP의 퍼즐라이프] '메달리온'과 4차원 미로
수학동아 2020.01.29 00:12
조회 2495
KPP와 함께하는
퍼즐라이프
퍼즐러가 사는 법
퍼즐을 좋아하는 사람들이 모인 단체
KPP _Korean Puzzle Party 멤버들이
매달 재밌고 유익한 퍼즐 이야기를 들려드립니다.
KPP와 함께 신기한 퍼즐을 살펴보고
그 속에 숨은 수학도 즐겨보세요!
--------------------------------
안녕하세요~.
‘퍼즐라이프’의 두 번째 주자인 KPP 멤버 ‘Eucleides’입니다.
제 닉네임은 수학자 유클리드의 그리스 이름에서 따왔으니
‘에우클레이데스’나 ‘유클리드’로 읽어주세요.
(본명은 비밀!)
오늘 제가 소개할 퍼즐은
독특한 미로가 새겨진 메달리온
1
국제 퍼즐 파티(IPP)와 교환 퍼즐
연예인들이 좀 더 잘 어울리는 이름으로 개명하듯, 메달리온도 처음엔 이름이 달랐습니다.
네덜란드의 퍼즐 디자이너 오스카 반 데벤터가 디자인한 ‘메달리온’은 2003년 미국 시카
고에서 열린 23번째 국제 퍼즐 파티(IPP)
국제 퍼즐 파티(International Puzzle Party) 는 전세계 퍼즐 수집가, 퍼즐 작가, 퍼즐 판매상 등이 매년 한자리에 모여 퍼즐에 관한 정보를 공유하고 새로 만든 퍼즐을 홍보하고 교환하는 퍼즐 축제. 퍼즐 교환 행사에 출품된 퍼즐을 그해의 교환 퍼즐 이라고 부른다.
현재는 퍼즐마스터를 위해 사진을 제공해 준 캐나다의 퍼즐 회사 퍼즐마스터(Puzzle Master)에서 판매하고 있는데요, 만약 여러분이 퍼즐 아래에 Puzzle Master 로고 대신 IMO로고가 있는 동일 퍼즐을 발견하신다면 당시 행사의 기념품으로 제작된 퍼즐을 찾으신 거예요!
메달리온의 모습. 메달처럼 생긴 본체 앞뒤로 금색, 은색 원판이 붙어있다. 원판에는 요상한 모양의 홈이 새겨졌다. 메달리온은 어떻게 즐기는 퍼즐일까?
출처: Puzzle Master Inc.
2
원판을 분리하라!
이제 메달리온를 분리해 어떤 목적을 가진 퍼즐인지 살펴보도록 하죠. 메달처럼 생긴 본체를 자세히 보면 반원 모양의 조각 2개가 맞물려 만들어졌고, 앞뒤로 삐쭉 튀어나온 '걸쇠'가 2개씩 있습니다. 메달리온의 처음 모습은 앞뒤에 달려있는 금색, 은색 원판에 새겨진 홈의 폭이 이 걸쇠의 지름보다 좁아서 끼어 분리되지 않는 상태입니다.
이제 감이 오죠? 메달리온의 목표는 원판을 본체로 부터 분리해내서 본체를 좌우로 당겨 두 조각으로 분리하는 겁니다. 그러기 위해서는 두 원판을 시계 또는 반시계방향으로 모두 돌려가며 걸쇠를 미로 끝의 구멍으로 옮겨야 합니다. 구멍의 지름은 걸쇠의 지름보다 커서 원판이 빠져나올 수 있거든요. 메달리온의 구조상 4개의 걸쇠는 반드시 동시에 구멍에 도착해야 합니다!
3
메달리온은 왜 4D였을까?
(feat. 극좌표 & 평면좌표)
그런데 메달리온의 원래 이름은 왜 ‘4D’였을까요?
‘극좌표’와 ‘평면 좌표’를 이용해 그 이유를 찾아가다 보면 이유와 더불어 메달리온의 해법을 찾을 수 있는 팁도 발견할 수 있습니다. 그러려면 우선 극좌표와 평면 좌표가 뭔지부터 알아야 합니다.
원점을 기준으로 수평 방향으로 떨어진 거리와 수직 방향으로 떨어진 거리를 순서쌍으로 나타낸 것을 평면 좌표 라고 합니다. 이와 달리 극좌표 는 원점과 점을 이은 선분이 만드는 각도와 길이로 점의 위치를 나타내는 방법으로, 원판에 새겨진 미로처럼 한 점을 기준으로 원형으로 배치된 대상의 정보를 나타낼 때 유용하죠.
서로 달라 보이지만, 필요에 따라 평면 좌표를 극좌표로, 극좌표를 평면 좌표로 바꿀 수 있습니다. 우리에겐 평면 좌표가 익숙하니 메달에 새겨진 미로를 평면 좌표로 나타내 보죠. 방법은 아래 그림을 참고하세요!
자, 이제 거의 다 왔습니다. 미로의 한 점을 나타내는 순서쌍에 주목해서 설명을 들어보세요.
두 미로는 한 원판 위에 새겨져 있기 때문에 원판을 회전하면 두 미로가 동시에 똑같은 정도로 회전합니다. 그래서 하나의 미로가 얼마나 움직인지 알면 다른 미로가 얼마나 움직였는지도 알 수 있죠. 마찬가지로 본체에 달려있는 걸쇠들도 동시에 같은 정도로 움직입니다.
결국 4개의 미로와 4개의 걸쇠는 2개씩 짝지을 수 있고, 미로를 떠도는 걸쇠의 상태는 4개의 좌표평면만 있어도 나타낼 수 있죠. 이 4개의 좌표만 있어도 우리는 아래 정보를 알아낼 수 있습니다!
❶ 금색 원판이 얼마나 회전했는가,
❷ 은색 원판이 얼마나 회전했는가,
❸ 본체의 왼쪽 조각이 얼마나 왼쪽으로 움직였는가,
❹ 본체의 오른쪽 조각이 얼마나 오른쪽으로 움직였는가
결국 메달리온의 현재 상태(원판의 상태, 걸쇠의 위치)는 총 4개 의 순서쌍으로 나타낼 수 있는 4차원 미로 인 셈입니다. 이름이 왜 4D 였는지 이제아시겠죠? 미로를 평면 좌표로 나타내면 걸쇠의 위치를 순서쌍으로 나타낼 수도 있어 해법을 찾기도 좋습니다.
이 방법으로 메달리온 풀기에 도전해보세요!
--------------------------------
함 께 풀 어 보 세 요
메달리온이 어떤 퍼즐인지 알겠죠?
내용을 이해했으면 아래 문제에 도전해보세요!
문제를 풀 아이디어 및 정답을 댓글로 달면
KPP 멤버가 직접 답변해 줍니다!
1.
극좌표를 평면 좌표로 나타내는 원리를 이용해
다른 미로도 사각형으로 바꿔보세요!
2.
본체의 두 조각은 길쭉한 부분을 통해 맞물려 있습니다.
이런 형태가 필요한 이유는 무엇일까요?
만약 길쭉한 부분이 지금보다 짧으면 어떤 문제가 생길까요?
3.
메달리온의 원리를 응용해 더 높은 차원의 미로 퍼즐을 만들 수 있을까요?
-끝-
지금 바로
로그인 하면 내가 찜한 문제와 수행 평가를 한곳에서 볼 수 있어요!
