수학동아 - 폴리매스

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

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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
Line: 17
Function: _error_handler

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

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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
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Function: getComment

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: 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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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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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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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: 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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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/index.php
Line: 315
Function: require_once

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Filename: core/Loader.php

Line Number: 925

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

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Filename: core/Loader.php

Line Number: 925

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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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Function: get_header

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

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Filename: core/Loader.php

Line Number: 925

Backtrace:

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
Line: 557
Function: get_header

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

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Severity: 8192

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Filename: core/Loader.php

Line Number: 925

Backtrace:

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/index.php
Line: 315
Function: require_once

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Filename: core/Loader.php

Line Number: 925

Backtrace:

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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Function: get_header

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

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Message: Creation of dynamic property CI_Loader::$articleStatus is deprecated

Filename: core/Loader.php

Line Number: 925

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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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Function: get_header

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

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Backtrace:

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
Line: 557
Function: get_header

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

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Severity: 8192

Message: Creation of dynamic property CI_Loader::$contents_model is deprecated

Filename: core/Loader.php

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Backtrace:

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
Line: 557
Function: get_header

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

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Filename: core/Loader.php

Line Number: 925

Backtrace:

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
Line: 557
Function: get_header

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

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Severity: 8192

Message: Creation of dynamic property CI_Loader::$common is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

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
Line: 557
Function: get_header

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

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Severity: 8192

Message: Creation of dynamic property CI_Loader::$dto is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

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
Line: 557
Function: get_header

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

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Severity: 8192

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Filename: core/Loader.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
Line: 557
Function: get_header

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

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Filename: ver3/Article_model.php

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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

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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

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Message: Creation of dynamic property Contents::$article_model is deprecated

Filename: core/Loader.php

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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

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Severity: 8192

Message: Creation of dynamic property CI_Loader::$article_model is deprecated

Filename: core/Loader.php

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Backtrace:

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

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

주니어 폴리매스 문제

수학 문제를 푸는 매력에 빠져 보세요!

[방승진 교수의 수학 퍼즐] 방7. 벤 다이어그램 숫자 퍼즐

수학동아 2019.02.01 09:43 조회 2859

페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

주니어 폴리매스를 시작하면서 아주대 수학과 방승진 교수님은 다음과 같은 조언을 해주셨습니다. 앞으로 교수님의 의견에 따라 문제를 풀어 보세요!

요즘 수학 문제는 일회용 물수건처럼 쓰고 버리는 것이라는 인상을 지울 수 없습니다. 학생들은 셀 수 없을 정도로 많은 수학 문제를 풀고 또 풀지만 수학 실력은 늘어나지 않습니다. 왜 일까요? 머리가 나빠서 일까요? 연구에 따르면 학생들은 누구나 잠재력이 있다고 합니다. 수학도 마찬가지 아닐까요?

제 경험에 의하면 수학 문제를 마치 껌 씹듯이 생각에 생각을 거듭하면 다양한 생각을 하게 되고 어느 덧 그 수학 문제는 영원히 잊지 않을 정도로 친숙하게 됩니다. 좀 더 정확하게 "어떤 문제를 푸는가도 중요하지만 문제를 어떻게 푸는가?" 가 더 중요합니다. 결국 문제를 풀고 난 뒤에 '어떤 창의적인 산출물을 만들었는가?' 가 중요합니다.

앞으로 게재하는 문제들은 주로 다양하게 생각하도록 유도하는 문제 즉, 개방형 문제(open-ended problem)로서 여러분들이 좀 더 창의적인 태도를 가질 수 있도록 안내할 겁니다.

모든 문제는 주어진 질문에 국한하지 말고 될 수 있는 한 일반화 시키고, 남들과는 다르게 생각하려고 노력해야 좋습니다. 수학 논문을 쓰면 더욱 좋습니다.

문제

아래 벤 다이어그램에는 a에서 g까지 7개 영역이 있다. 각 알파벳에 1에서 7까지의 자연수를 1개씩 대응시켜 모든 원 안의 수의 합이 같게 하고 싶다. 이런 경우를 모두 구하여라.

이전글 방6. 알쏭달쏭 종이접기

다음글 방8. 모호한 사각형

문제 찜하기 목록보기

댓글 작성하기

happian Lv.1 2019.02.06 20:31

a : 1    b : 2    c : 3    d : 4    e : 7    f : 5    g : 6
a : 1    b : 2    c : 4    d : 3    e : 6    f : 5    g : 7
a : 1    b : 2    c : 4    d : 6    e : 7    f : 3    g : 5
a : 1    b : 2    c : 6    d : 4    e : 5    f : 3    g : 7
a : 1    b : 3    c : 2    d : 4    e : 7    f : 6    g : 5
a : 1    b : 3    c : 4    d : 2    e : 5    f : 6    g : 7
a : 1    b : 3    c : 5    d : 7    e : 6    f : 2    g : 4
a : 1    b : 3    c : 7    d : 5    e : 4    f : 2    g : 6
a : 1    b : 4    c : 2    d : 3    e : 6    f : 7    g : 5
a : 1    b : 4    c : 2    d : 6    e : 7    f : 5    g : 3
a : 1    b : 4    c : 3    d : 2    e : 5    f : 7    g : 6
a : 1    b : 4    c : 6    d : 2    e : 3    f : 5    g : 7
a : 1    b : 5    c : 3    d : 7    e : 6    f : 4    g : 2
a : 1    b : 5    c : 6    d : 7    e : 4    f : 2    g : 3
a : 1    b : 5    c : 7    d : 3    e : 2    f : 4    g : 6
a : 1    b : 5    c : 7    d : 6    e : 3    f : 2    g : 4
a : 1    b : 6    c : 2    d : 4    e : 5    f : 7    g : 3
a : 1    b : 6    c : 4    d : 2    e : 3    f : 7    g : 5
a : 1    b : 6    c : 5    d : 7    e : 4    f : 3    g : 2
a : 1    b : 6    c : 7    d : 5    e : 2    f : 3    g : 4
a : 1    b : 7    c : 3    d : 5    e : 4    f : 6    g : 2
a : 1    b : 7    c : 5    d : 3    e : 2    f : 6    g : 4
a : 1    b : 7    c : 5    d : 6    e : 3    f : 4    g : 2
a : 1    b : 7    c : 6    d : 5    e : 2    f : 4    g : 3
a : 2    b : 1    c : 4    d : 5    e : 7    f : 3    g : 6
a : 2    b : 1    c : 5    d : 4    e : 6    f : 3    g : 7
a : 2    b : 3    c : 6    d : 7    e : 5    f : 1    g : 4
a : 2    b : 3    c : 7    d : 6    e : 4    f : 1    g : 5
a : 2    b : 4    c : 1    d : 5    e : 7    f : 6    g : 3
a : 2    b : 4    c : 5    d : 1    e : 3    f : 6    g : 7
a : 2    b : 5    c : 1    d : 4    e : 6    f : 7    g : 3
a : 2    b : 5    c : 4    d : 1    e : 3    f : 7    g : 6
a : 2    b : 6    c : 3    d : 7    e : 5    f : 4    g : 1
a : 2    b : 6    c : 7    d : 3    e : 1    f : 4    g : 5
a : 2    b : 7    c : 3    d : 6    e : 4    f : 5    g : 1
a : 2    b : 7    c : 6    d : 3    e : 1    f : 5    g : 4
a : 3    b : 1    c : 4    d : 6    e : 7    f : 2    g : 5
a : 3    b : 1    c : 6    d : 4    e : 5    f : 2    g : 7
a : 3    b : 2    c : 5    d : 7    e : 6    f : 1    g : 4
a : 3    b : 2    c : 7    d : 5    e : 4    f : 1    g : 6
a : 3    b : 4    c : 1    d : 6    e : 7    f : 5    g : 2
a : 3    b : 4    c : 6    d : 1    e : 2    f : 5    g : 7
a : 3    b : 5    c : 2    d : 7    e : 6    f : 4    g : 1
a : 3    b : 5    c : 7    d : 2    e : 1    f : 4    g : 6
a : 3    b : 6    c : 1    d : 4    e : 5    f : 7    g : 2
a : 3    b : 6    c : 4    d : 1    e : 2    f : 7    g : 5
a : 3    b : 7    c : 2    d : 5    e : 4    f : 6    g : 1
a : 3    b : 7    c : 5    d : 2    e : 1    f : 6    g : 4
a : 4    b : 1    c : 2    d : 3    e : 7    f : 5    g : 6
a : 4    b : 1    c : 3    d : 2    e : 6    f : 5    g : 7
a : 4    b : 2    c : 1    d : 3    e : 7    f : 6    g : 5
a : 4    b : 2    c : 3    d : 1    e : 5    f : 6    g : 7
a : 4    b : 3    c : 1    d : 2    e : 6    f : 7    g : 5
a : 4    b : 3    c : 2    d : 1    e : 5    f : 7    g : 6
a : 4    b : 5    c : 6    d : 7    e : 3    f : 1    g : 2
a : 4    b : 5    c : 7    d : 6    e : 2    f : 1    g : 3
a : 4    b : 6    c : 5    d : 7    e : 3    f : 2    g : 1
a : 4    b : 6    c : 7    d : 5    e : 1    f : 2    g : 3
a : 4    b : 7    c : 5    d : 6    e : 2    f : 3    g : 1
a : 4    b : 7    c : 6    d : 5    e : 1    f : 3    g : 2
a : 5    b : 1    c : 3    d : 6    e : 7    f : 2    g : 4
a : 5    b : 1    c : 6    d : 3    e : 4    f : 2    g : 7
a : 5    b : 2    c : 4    d : 7    e : 6    f : 1    g : 3
a : 5    b : 2    c : 7    d : 4    e : 3    f : 1    g : 6
a : 5    b : 3    c : 1    d : 6    e : 7    f : 4    g : 2
a : 5    b : 3    c : 6    d : 1    e : 2    f : 4    g : 7
a : 5    b : 4    c : 2    d : 7    e : 6    f : 3    g : 1
a : 5    b : 4    c : 7    d : 2    e : 1    f : 3    g : 6
a : 5    b : 6    c : 1    d : 3    e : 4    f : 7    g : 2
a : 5    b : 6    c : 3    d : 1    e : 2    f : 7    g : 4
a : 5    b : 7    c : 2    d : 4    e : 3    f : 6    g : 1
a : 5    b : 7    c : 4    d : 2    e : 1    f : 6    g : 3
a : 6    b : 1    c : 2    d : 5    e : 7    f : 3    g : 4
a : 6    b : 1    c : 5    d : 2    e : 4    f : 3    g : 7
a : 6    b : 2    c : 1    d : 5    e : 7    f : 4    g : 3
a : 6    b : 2    c : 5    d : 1    e : 3    f : 4    g : 7
a : 6    b : 3    c : 4    d : 7    e : 5    f : 1    g : 2
a : 6    b : 3    c : 7    d : 4    e : 2    f : 1    g : 5
a : 6    b : 4    c : 3    d : 7    e : 5    f : 2    g : 1
a : 6    b : 4    c : 7    d : 3    e : 1    f : 2    g : 5
a : 6    b : 5    c : 1    d : 2    e : 4    f : 7    g : 3
a : 6    b : 5    c : 2    d : 1    e : 3    f : 7    g : 4
a : 6    b : 7    c : 3    d : 4    e : 2    f : 5    g : 1
a : 6    b : 7    c : 4    d : 3    e : 1    f : 5    g : 2
a : 7    b : 1    c : 2    d : 3    e : 6    f : 4    g : 5
a : 7    b : 1    c : 3    d : 2    e : 5    f : 4    g : 6
a : 7    b : 1    c : 3    d : 5    e : 6    f : 2    g : 4
a : 7    b : 1    c : 5    d : 3    e : 4    f : 2    g : 6
a : 7    b : 2    c : 1    d : 3    e : 6    f : 5    g : 4
a : 7    b : 2    c : 3    d : 1    e : 4    f : 5    g : 6
a : 7    b : 2    c : 4    d : 6    e : 5    f : 1    g : 3
a : 7    b : 2    c : 6    d : 4    e : 3    f : 1    g : 5
a : 7    b : 3    c : 1    d : 2    e : 5    f : 6    g : 4
a : 7    b : 3    c : 1    d : 5    e : 6    f : 4    g : 2
a : 7    b : 3    c : 2    d : 1    e : 4    f : 6    g : 5
a : 7    b : 3    c : 5    d : 1    e : 2    f : 4    g : 6
a : 7    b : 4    c : 2    d : 6    e : 5    f : 3    g : 1
a : 7    b : 4    c : 5    d : 6    e : 3    f : 1    g : 2
a : 7    b : 4    c : 6    d : 2    e : 1    f : 3    g : 5
a : 7    b : 4    c : 6    d : 5    e : 2    f : 1    g : 3
a : 7    b : 5    c : 1    d : 3    e : 4    f : 6    g : 2
a : 7    b : 5    c : 3    d : 1    e : 2    f : 6    g : 4
a : 7    b : 5    c : 4    d : 6    e : 3    f : 2    g : 1
a : 7    b : 5    c : 6    d : 4    e : 1    f : 2    g : 3
a : 7    b : 6    c : 2    d : 4    e : 3    f : 5    g : 1
a : 7    b : 6    c : 4    d : 2    e : 1    f : 5    g : 3
a : 7    b : 6    c : 4    d : 5    e : 2    f : 3    g : 1
a : 7    b : 6    c : 5    d : 4    e : 1    f : 3    g : 2
총 108개 입니다.

댓글 작성하기 좋아요0 댓글수5
- 아인수타인 Lv.12 2019.02.07 10:01
  
  헠 뭐가 이렇게 많지...
  
  좋아요0
- happian Lv.1 2019.02.07 19:15
  
  좀 많죠 - -;;
  
  좋아요0
- 아루키데메스 Lv.5 2019.02.10 04:13
  
  너무 많네요.108가지니까..
  
  좋아요0
- 뉴＿턴 Lv.8 2019.10.04 23:55
  
  우와!! 찾기 엄청 힘들었겠네요!!
  
  좋아요0
- BLUESPEAR Lv.5 2020.05.19 17:39
  
  근데 이게 다 합이 같게 한 경우인가요?
  
  좋아요0

아루키데메스 Lv.5 2019.02.25 18:55

확인요청중

a+b+c+d+e+f+g+2a+b+c+d=3으로 나눠지는 수

a+b+c+d+e+f+g=28

a b c d

1 2 3 4 1+1+2+3+4+28=39 39/3=13 ----1

2 3 4 5 2+2+3+4+5+28=44 44/3=14...2(x)

3 4 5 6 3+3+4+5+6+28=49 49/3=16...1(x)

4 5 6 7 4+4+5+6+7+28=54 54/3=18 ----2

7 6 5 4 7+7+6+5+4+28=57 57/3=19 ----3

6 5 4 3 6+6+5+4+3+28=52 52/3=17...1(x)

5 4 3 2 5+5+4+3+2+28=47 47/3=15...2(x)

4 3 2 1 4+4+3+2+1+28=42 42/3=14 ----4

1.e=13-6=7

f=13-8=5

g=13-7=6

2.e=18-15=3

f=18-17=1

g=18-16=2

3.e=18-15=3

f=18-17=1

g=18-16=2

4.e=14-9=5

f=14-7=7

g=14-8=6

<답> 이렇게 4가지 나오네요.

	a	b	c	d	e	f	g
1.	1	2	3	4	7	5	6
2.	4	5	6	7	3	1	2
3.	7	6	5	4	1	3	2
4.	4	3	2	1	5	7	6

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아인수타인 Lv.12 2019.03.01 09:24

벤다이어그램의 원을 4개로 바꾼다면 어떻게 될까요? 원 n개에 대해 일반화할 순 없을까요? (원 4개로는 그릴 수 없긴 하지만 찌그러진 호빵 모양을 같이 이용하면 그릴 수 있습니다.)

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