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
Line: 315
Function: require_once

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
Line: 315
Function: require_once

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
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::$hooks is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

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::$config is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

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::$log is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

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::$utf8 is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

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::$uri is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

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::$exceptions is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

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::$router is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

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::$output is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

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::$security is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

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::$input is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

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::$lang is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

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::$load is deprecated

Filename: core/Controller.php

Line Number: 78

Backtrace:

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::$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::$cache is deprecated

Filename: core/Loader.php

Line Number: 1279

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::$cacher is deprecated

Filename: core/Loader.php

Line Number: 1279

Backtrace:

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::$jscript is deprecated

Filename: core/Loader.php

Line Number: 1279

Backtrace:

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: 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
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: 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
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: 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
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: 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
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: 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
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: 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
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: 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
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: 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
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: 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
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: 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
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: 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
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: 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
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: 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
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: 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
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: 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
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: 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
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: 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
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::$session is deprecated

Filename: core/Loader.php

Line Number: 1279

Backtrace:

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::$agent is deprecated

Filename: core/Loader.php

Line Number: 1279

Backtrace:

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::$contentsStatus is deprecated

Filename: libraries/Common.php

Line Number: 64

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 64
Function: _error_handler

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 24
Function: initContentsStatusInfo

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::$articleStatus is deprecated

Filename: libraries/Common.php

Line Number: 71

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 71
Function: _error_handler

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 24
Function: initContentsStatusInfo

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::$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
Line: 15
Function: database

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_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
Line: 15
Function: database

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::$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 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
Line: 20
Function: model

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::$contents_model is deprecated

Filename: core/Loader.php

Line Number: 353

Backtrace:

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::$menuList is deprecated

Filename: libraries/Common.php

Line Number: 561

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 561
Function: _error_handler

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::$common is deprecated

Filename: core/Loader.php

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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

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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

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File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
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Line: 799
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File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
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Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
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File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
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Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
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File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
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Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
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File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
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Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
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File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 387
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
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File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 387
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
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Line: 315
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File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 387
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
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Line: 387
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
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Function: _error_handler

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
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File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
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Function: _error_handler

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

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
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Line: 434
Function: view

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Line: 315
Function: require_once

수학동아 - 폴리매스
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폴리매스 문제
아직 아무도 답을 모르는 문제에 도전하세요!
[국가수리과학연구소] 국5. 혼자 하는 카드게임의 승률은?
수학동아 2017.05.20 21:35 조회 3770
공유하기
페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

국가수리과학연구소 5번

 

혼자 하는 카드게임의 승률은?

                 

 

문제 출제자 : 이석형 수리과학연구소 연구원

 

 

52장의 트럼프 카드에는 4가지 문양에 숫자가 1부터 13까지 있습니다. A, J, Q, K를 각각 1, 11, 12, 13으로 간주하면 됩니다.

그리고 이 트럼프 카드로 혼자 하는 놀이인 솔리테르(solitaire) 중 다음과 같은 것을 생각합니다.

 

ⒸBetzaar

 

트럼프 카드 52장을 임의로 섞고, 한 장 한 장 카드를 넘기면서 "A(1), 2, 3, 4, … , 10, J(11), Q(12), K(13), A(1), …"이런 식으로 불러나갑니다. 카드를 넘길 때 자신이 부르는 숫자가 그 카드에 있으면(예를 들어, 첫 번째 카드가 A이거나 3번째 혹은 3+13=16번째 카드가 3이거나) 솔리테르에 실패하고, 카드 52장을 모두 넘기는 동안 그런 경우가 없으면 솔리테르에 성공합니다.

 

(1) 위를 일반화해서 k가지 문양에 1부터 n까지의 숫자가 있는 경우를 생각합니다. 트럼프 카드는 k=4, n=13인 경우가 되겠지요. k가 고정돼 있고 n이 무한대로 갈 때, 솔리테르에 성공할 확률은 얼마로 수렴할까요? k=1, 2, 3, 4에 대해서 먼저 성공 확률을 구해 보고, n인 경우에 대해 구해 봅시다.

 

(2) 트럼프 카드의 경우 솔리테르에 성공할 확률을 소수점 6째 자리까지 계산해 보세요.

 

<알립니다>

'수학자'님이 국가수리과학연구소의 5번 문제를 완벽하게 해결했습니다. 

풀이법이 궁금한 독자는 '수학자'님의 블로그를 참고해 주세요.

 

문제를 완벽 해결한 두 번째 MVP '수학자' 님을 

수학동아에서 소개할 날을 기다릴게요.

'수학자' 님은 이 공지를 보시면 비밀댓글로 연락처를 남겨주세요! 

 

'수학자' 풀이법 바로보기 

http://blog.naver.com/cozyyg/221012336908

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  •  
    에프매스 2017.05.22 22:44

    [mathdonga.blog.me에서 옮겨 온 댓글입니다]

    수학책갈피2017.05.02. 09:23

    그러니까....
    트럼프 카드의 경우는, 카드가 나온 순서 ≠ 그 카드의 숫자(mod 13)이고
    (1)문제의 경우에는, 카드가 나온 순서는 1~nk, 카드의 숫자는 1~k가 되겠군요..

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      에프매스 2017.05.22 22:45

      [mathdonga.blog.me에서 옮겨 온 댓글입니다]

      수학책갈피2017.05.02. 09:25

      사건 = 순서를 k단위로 묶은 후 카드의 '숫자만' 규칙에 맞게 정해주고 문양을 정해준다
      전체 = 걍 (kn)!

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    •  
      로보카폴리 Lv.11 2019.10.08 08:21

      왜 9레벨이에요?

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  •  
    에프매스 2017.05.22 22:46

    [mathdonga.blog.me에서 옮겨 온 댓글입니다]

    tommy2017.05.02. 22:03

    k=1이면 그냥 완전순열의 개수 구하기 문제 아닌가요? n!으로 나눠주면 확률은 바로 나오니까요
    근데 폴리매쓰 문제 풀 때 다른 책 참고해도 괜찮은가요? ;; 책에서 완전순열 공식을 봤던 것 같은데..

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    에프매스 2017.05.22 22:46

    [mathdonga.blog.me에서 옮겨 온 댓글입니다]

    tommy2017.05.02. 22:06

    근데 (1)의 끝부분에서 'n인 경우에 대해 구해 봅시다'는 무슨 뜻이죠? k=n일 때 n을 무한대로 보내면 수렴값이 어떻게 되냐는 건가요?

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    •  
      에프매스 2017.05.22 22:47

      [mathdonga.blog.me에서 옮겨 온 댓글입니다]

      elusive11022017.05.02. 22:52

      K의 1,2,3,4확률을 구하고, N이 1~13일때의 확률도 구하라는 뜻 같은데요ㅎㅎ
      (간만에 이해할수 있는 문제나온 초딩)

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      에프매스 2017.05.22 23:36

      [mathdonga.blog.me에서 옮겨 온 댓글입니다]

      tommy2017.05.02. 23:29

      elusive1102  

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      에프매스 2017.05.22 23:37

      [mathdonga.blog.me에서 옮겨 온 댓글입니다]

      수학책갈피2017.05.06. 13:31

      n과 k 에대한 솔리테르 일반식을 만들라는 소리 아닌가요?

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      에프매스 2017.05.22 23:38

      [mathdonga.blog.me에서 옮겨 온 댓글입니다]

      tommy2017.05.08. 23:23

      수학책갈피아.. 그럴지도 모르겠군요. 표현이 좀 애매하긴 하지만요ㅎㅎ;

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    에프매스 2017.05.22 23:15

    [mathdonga.blog.me에서 옮겨 온 댓글입니다]

    elusive11022017.05.02. 23:36

    계산해 봤는데...
    그럼 K가 1일때 확률은 약 93.013562퍼센트
    아니에요?

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    •  
      에프매스 2017.05.22 23:17

      [mathdonga.blog.me에서 옮겨 온 댓글입니다]

      tommy2017.05.02. 23:41

      n을 무한대로 보낼 때요?

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      에프매스 2017.05.22 23:18

      [mathdonga.blog.me에서 옮겨 온 댓글입니다]

      tommy2017.05.02. 23:49

      책 참고해도 되는지 모르겠지만.. '리스 하스아우트'라는 분이 쓰신 '범죄 수학'에 이 내용이 나오네요. 내용은 저 문제에 맞게 해석하면 k=1일 때 n을 무한대로 보내면 확률은 1/e(즉 약 36.787944%)가 된다는 내용입니다

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      에프매스 2017.05.22 23:20

      [mathdonga.blog.me에서 옮겨 온 댓글입니다]

      키퍼2017.05.10. 16:37

      tommy오...저도 그책봤는데.... 그거 구하는 공식 알면 쉬울것 같은데....

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      에프매스 2017.05.22 23:21

      [mathdonga.blog.me에서 옮겨 온 댓글입니다]

      tommy2017.05.12. 22:21

      키퍼풀이도 나와 있긴 해요ㅎ

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      에프매스 2017.05.22 23:22

      [mathdonga.blog.me에서 옮겨 온 댓글입니다]

      키퍼2017.05.13. 11:34

      tommy근데 2일떄는 안나와 있더라구요.....

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      에프매스 2017.05.22 23:23

      [mathdonga.blog.me에서 옮겨 온 댓글입니다]

      tommy2017.05.14. 12:06

      키퍼그때는 단순히 완전순열 문제가 아니니까요...

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      에프매스 2017.05.22 23:23

      [mathdonga.blog.me에서 옮겨 온 댓글입니다]

      키퍼2017.05.14. 19:40

      tommy프로그레밍이라도 알면 뭐라도하는데....프로그레밍은 하나도몰라서.... ㅠㅠ

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      에프매스 2017.05.22 23:24

      [mathdonga.blog.me에서 옮겨 온 댓글입니다]

      tommy2017.05.18. 23:32

      키퍼기회가 되시면 한 번 배워 보세요ㅎㅎ SCRATCH라는 언어는 아이들용 언어라서 배우기 쉬우실 거예요^^

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    에프매스 2017.05.22 23:25

    [mathdonga.blog.me에서 옮겨 온 댓글입니다]

    수학책갈피2017.05.06. 13:29

    프로그래밍을 통한 풀이가 거의 완료되었습니다.... (2)번

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      에프매스 2017.05.22 23:26

      [mathdonga.blog.me에서 옮겨 온 댓글입니다]

      tommy2017.05.08. 23:25

      잠시만요.. 트럼프 카드를 배열할 수 있는 경우의 수는 52!=80658175170943878571660636856403766975289505440883277824000000000000가지잖아요.. 그걸 다 따질 수 있나요..?

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      에프매스 2017.05.22 23:27

      [mathdonga.blog.me에서 옮겨 온 댓글입니다]

      수학책갈피2017.05.13. 23:06

      tommy맞아욬ㅋ
      컴퓨터의 한계로 풀이가 실패했네요ㅠㅠ
      기초적인 경우의 수도 안따지고 들어가다니...

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      에프매스 2017.05.22 23:27

      [mathdonga.blog.me에서 옮겨 온 댓글입니다]

      tommy2017.05.14. 12:08

      수학책갈피허걱ㅋ
      뭐 그래도 1~13이 4번 반복되니까 단순 52!보다는 가짓수가 줄어들 것 같긴 하지만.. 어쨌든 가짓수가 굉장히 많을 테니까요ㅎㅎ

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    에프매스 2017.05.22 23:28

    [mathdonga.blog.me에서 옮겨 온 댓글입니다]

    Lucky star2017.05.18. 22:49

    저도 c언어로는 포기...

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    에프매스 2017.05.22 23:29

    [mathdonga.blog.me에서 옮겨 온 댓글입니다]

    Lucky star2017.05.18. 22:50

    근데 한 숫자가 나올 확률 == 4 / 52니까,

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    에프매스 2017.05.22 23:29

    [mathdonga.blog.me에서 옮겨 온 댓글입니다]

    Lucky star2017.05.18. 22:52

    1은 13 / 52, 즉 1 / 13이고,

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    에프매스 2017.05.22 23:29

    [mathdonga.blog.me에서 옮겨 온 댓글입니다]

    Lucky star2017.05.18. 22:57

    2는 51가지 중에 2가 남아있는 수가 몇 개 인지가 문제인데...

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    에프매스 2017.05.22 23:30

    [mathdonga.blog.me에서 옮겨 온 댓글입니다]

    Lucky star2017.05.18. 23:00

    2가 3개 있을 확률은 4 / 48 == 1 / 12.
    2가 4개 있을 확률은 44 / 48 == 11 / 12.

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    에프매스 2017.05.22 23:30

    [mathdonga.blog.me에서 옮겨 온 댓글입니다]

    Lucky star2017.05.18. 23:00

    ....

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  •  
    에프매스 2017.05.22 23:31

    [mathdonga.blog.me에서 옮겨 온 댓글입니다]

    ogyikk2017.05.20. 21:40

    ㅇㅇ
    ㅇ

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  •  
    에프매스 2017.05.30 18:46

    수학자2017.05.23. 15:23

    http://blog.naver.com/cozyyg/221012336908
    (1) 풀었습니다. 답의 형태로 보아 더 좋은 풀이가 있을지는 잘 모르겠습니다.
    (2)는 Step 1의 내용을 적용해주면 구할 수 있습니다. 울프럼 알파로 구해보면 답은 0.016233입니다.

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    •  
      에프매스 2017.05.30 18:47

      수학동아2017.05.24. 14:23

      축하합니다! '수학자'님의 (1), (2) 답이 모두 맞았습니다. 오랜만에 MVP가 탄생했네요!

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