$\underline{\text { Zhenedarov R.G. }}$

Two pirates, Bill and John, each having 74 gold coins, decided to play such a game: they will take turns laying coins on the table, one, two, or three at a time, and the one who places the hundredth coin in sequence will win. Bill starts. Who can win this game, regardless of how the opponent acts?
If the pirates had an unlimited number of coins, John's winning strategy would be simple: on any move by Bill, he would only need to add enough coins to make the total four.

Indeed, in this case, the number of coins after each of John's moves would be a multiple of four, and since 100 is divisible by 4, John would be able to place the hundredth coin on his twenty-fifth move.

However, the pirates each have only 74 coins, so if Bill places one coin each time, John would have to place three coins each move, and by the twenty-fifth move, John would run out of coins. Therefore, to maintain such a winning strategy, John must at some point place one or two coins. Let's show that this is possible.

If Bill places two or three coins on his first move, John will save coins on the first move and win. Suppose Bill places one coin on his first move. Then John will also place one coin in response. There are three possible scenarios for Bill's second move:

1) Bill places one coin. Then John will also place one coin. There will be four coins on the table, and from then on, John can apply the strategy described above—he will have enough coins to win.
2) Bill places three coins. Then John will also place three coins. There will be eight coins on the table, and John will have already placed fewer than three coins once, so he can apply the strategy described above and win.
3) Bill places two coins. Then there will be four coins on the table. John will place one coin. Bill must not allow the number of coins on the table to be a multiple of 4 after John's move, so he must place three coins. Each subsequent move, John will place one coin, forcing Bill to place three. However, Bill will not be able to place the hundredth coin, as he would need 75 coins. Therefore, John will place the hundredth coin.

## Answer

John.