Fun challenge! I'm an experienced Engineer who is eager to build this app for you in just 3 days! Quick and reliable delivery.
Steps to implement this project:
1) Design a friendly User-Interface (either Website/mobile app, up to you) for your group/friends to play the game
2) Create a leaderboard with a point-system, levelling-up, or any form of gamifying and keeping track of score of your preference
3) Build the algorithm behind the game, keep track of highest score, persist data in a storage and present to the UI
Happy to deliver this project to you in 3 days, I'd need a few clarifications regrading:
1) Should there be a website as UserInterface, or mobile app ? If mobile, which platform (android/iPhone?)
2) Should the user be able to login?
a) if not, are the users predetermined, i.e. names given in advance before app is built ?
b) If login page is desirable, should the user provide a username and password (any other information)? This way, the app can be extended and played by any number of users
Let me know if you'd like me to build this application for you. It would be my pleasure.
Kind regards