Question 77
Eight boxes numbered $1$ to $8$ stand in a row, together with an empty bag. Initially every box contains one token. Miha has a large supply of tokens and plays a game with these two allowed moves:
- Remove one token from box $i$ ($i\lt8$) and add two tokens to box $i+1$.
- Remove one token from box $i$ ($i\lt8$) and move one token from box $i+1$ into the bag.
The game ends when no move is possible. What is the greatest possible number of tokens in the bag at the end?
- Remove one token from box $i$ ($i\lt8$) and add two tokens to box $i+1$.
- Remove one token from box $i$ ($i\lt8$) and move one token from box $i+1$ into the bag.
The game ends when no move is possible. What is the greatest possible number of tokens in the bag at the end?