# Project Euler Problem 444 – The Roundtable Lottery

This blog tries to explain the lottery game in problem 444 of Project Euler. Please don’t read any further if you have yet to attempt to solve the problem on your own. The information is intended for those who failed to solve the problem and are looking for hints. It is posted not before the problem has a hundred solvers already.

## Lottery Game

This is one potential course of the game with six players, where every player plays optimally:

• Player 1 scratches his ticket and uncovers 2£.
• Player 2 trades her unscratched ticket with player 1 and leaves the game with 2£. Player 1 scratches the ticket and uncovers 6£.
• Player 3 trades his unscratched ticket with player 1 and leaves the game with 6£. Player 1 scratches the ticket and uncovers 3£.
• Player 4 trades her unscratched ticket with player 1 and leaves the game with 3£. Player 1 scratches the ticket and uncovers 1£.
• Player 5 scratches his ticket and uncovers 5£.
• Player 6 trades her unscratched ticket with player 5 and leaves the game with 5£. Player 4 scratches the ticket and uncovers 4£.

The game ends with two players seated at the table.