How to play Archimedes

Archimedes is a naval battle on a square grid. Each side commands a fleet of ships that sail like chess queens, but no ship ever captures by landing on another. Instead, a ship is sunk when three enemy ships have it in their sights at the same time, as if their combined fire had set it ablaze. The name recalls the legend of Archimedes setting enemy ships on fire with mirrors during the defence of Syracuse.

Because sinking takes three ships working together, the game is about coordination and lines of sight. Nothing is random: you win by spotting where lines cross and keeping your own ships out of danger.

How to play on skill.games

• Start a game. The settings window opens first: choose a difficulty and a board size, then press PLAY.
• Make a move. Tap one of your ships. Green dots show every square it can sail to. Tap one to move, or tap a different ship to change your mind.
• Sinking. When a ship is sunk, red lines flash from the three or more ships that sank it.
• Who moves first. Your fleet starts in the bottom-left corner, and you always make the first move.
• The score line at the top shows how many ships each side has left.
• Pause. The menu button in the top-left corner pauses the game, with options to resume, start a new game or switch the sound off.
• Saving. Your game is saved after every move. If you leave mid-game, choose CONTINUE next time to pick up where you stopped.
• Results. The end screen shows how many ships each side sank, what decided the game and how many moves were played, plus your wins, losses, draws, win rate and streaks for that board and difficulty.

Rules

Setup. Each fleet starts packed into a triangle in its own corner of the board: yours bottom-left, the computer's top-right. The very corner square of each triangle is left empty. Fleets have 7 ships on 6 × 6, 12 on 8 × 8 and 18 on 10 × 10.

Moving. On your turn you move one ship any number of squares in a straight line, horizontally, vertically or diagonally, like a queen in chess. It may only pass over and land on empty squares. Ships never jump or capture by landing.

Line of sight. A ship "sees" along its eight directions: up, down, left, right and the four diagonals. In each direction it sees only the first ship in that line, at any distance. Any ship, friend or enemy, blocks the view beyond it.

Sinking. After every move, each ship on the board is checked. Any ship that sees three or more enemy ships is sunk and removed. This applies to both colours:

• you can sink an enemy ship by moving a third ship into line with it;
• a ship you move into a square watched by three enemy ships is sunk at once;
• moving a ship out of the way can open a line of sight and get a ship sunk, yours or theirs.

All ships that qualify are removed together, even if one of them was helping to sink another. Their removal can open new lines of sight, so the check repeats until nothing more sinks.

Winning.

1. A side with fewer than three ships loses, since it can no longer sink anything. If both fleets fall below three ships in the same move, the game is a draw.
2. A player who has no legal move on their turn loses.
3. If 50 moves in a row (25 each) pass without any ship being sunk, the game ends: the side with more ships wins, and equal fleets make a draw.

Some versions of Archimedes add a home port that the enemy can try to enter. This version is played without ports: the battle is decided by sinking ships alone.

Strategy tips

• Count the watchers. Before moving, look along all eight lines from the destination square. If three of them end in an enemy ship, your ship is lost on arrival.
• Use friendly ships as shields. Your own ships block enemy sight. A ship tucked behind a friend is safe from that direction, so keep your fleet in mutually shielding clusters.
• Build a crossfire. Two of your ships already watching one enemy ship is a threat. Look for the move that brings in the third.
• Watch the squares you leave. Moving a ship that was blocking a line can expose the ship behind it. Check what each of your ships sees after the move, not just the ship that moved.
• Chain reactions work both ways. One sinking can open lines that sink more ships, including yours.
• Play for the numbers. If no one sinks a ship for 50 moves, the bigger fleet wins. When you are ahead, keep your ships safe; when you are behind, you have to force the action.

Difficulty levels

• Easy looks only at its own move, and about a third of its moves are random, so it leaves ships exposed fairly often.
• Normal looks at its move and your reply, and only occasionally plays a random move.
• Hard looks as far as Normal but almost never plays a random move, so it rarely leaves a ship hanging.
• Crazy looks the furthest ahead and never plays a random move. Every level always takes a winning move when it sees one.

Modes

Three board sizes are offered:

• 6 × 6, Quick with 7 ships each. The fleets start close together, so battles are short and sharp. This is the default.
• 8 × 8, Classic with 12 ships each, with more room to set up crossfires.
• 10 × 10, Big with 18 ships each. A long campaign where keeping your fleet organised matters most.

Statistics are kept separately for each board and difficulty.