Question 175
A game of coins is played as follows: You start with $1$ head and $1$ tail on a table. At each turn, you can perform any one of the following moves:
a. You can turn over all the coins on the table.
b. You can triple the numbers of heads and tails on the table.
c. If there are at least $4$ tails on the table, you can turn over $4$ tails.
d. If there are at least $5$ tails on the table, you can turn over $3$ of the tails and discard $2$ of the tails.
Knowing that at the end of a game you have $2024$ heads, what are the possible numbers of tails at the end of that game?
a. You can turn over all the coins on the table.
b. You can triple the numbers of heads and tails on the table.
c. If there are at least $4$ tails on the table, you can turn over $4$ tails.
d. If there are at least $5$ tails on the table, you can turn over $3$ of the tails and discard $2$ of the tails.
Knowing that at the end of a game you have $2024$ heads, what are the possible numbers of tails at the end of that game?