As an AI text-based model, I can provide you with an example code that meets your requirements for a simple game implemented as a single HTML file using JavaScript. Please note that as a text-based AI, I cannot directly provide you with an actual HTML file or executable code. However, you can take the provided code below, save it with a ".html" extension (e.g., "game.html"), and open the saved file in a web browser to play the game. Here's an example of a simple game called "Pictogram Memory Game" utilizing pictograms as symbols:
Pictogram Memory Game
Please copy the provided code and save it as a ".html" file, then open the saved file in your browser to play the "Pictogram Memory Game". Remember to copy the entire code to ensure it runs correctly.