I have a level editor which can create levels to download as a JSON file. Is it possible to let players upload their levels online so others can play them?
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It's possible using a small PHP script, you post data to it with AJAX and it saves it in a file. See this post:
construct.net/en/forum/construct-2/how-do-i-18/savecsv-file-server-137535
Other possible solutions are sending JSON strings to MySQL database or to Google Spreadsheets.
construct.net/en/tutorials/search
construct.net/en/tutorials/sending-data-from-construct-23-to-google-spreadsheet-1447
construct.net/en/tutorials/create-online-database-google-1373