Counterweight

Goal

Every scale is perfectly balanced. It carries symbols of unknown weight, sometimes with standard weights marked with a number. By reasoning from one scale to the next, work out what each symbol weighs, then say what must go on the final scale (the one with the golden frame) to balance it. Every puzzle has exactly one solution and can be solved by deduction: you never have to guess.

How it works

• Tap a symbol in the notebook: all its appearances light up. Then type the weight you deduced on the keypad. It is just a note and costs nothing.
• Check my notes (three times per puzzle) marks each note as right or wrong, without giving the correct value.
• On the final scale, enter the total on the keypad (golden token), or switch to Symbols mode to place symbols on the free pan yourself. Symbols already on the left pan are then not available.
• Tap Weigh: the final scale stays locked until then. If it balances, you win; otherwise it tips towards the heavier side and the missed weighing counts as a mistake.
• Hint (H key): first the useful scale, then the reasoning, finally the weight of a symbol. Each step costs time.

Stars and time

• Three stars with no penalty, two up to two penalties, one beyond that. A missed weighing or a hint that reveals a weight counts as one penalty.
• A hint’s reasoning step and each penalty also add seconds to the clock: records take this into account.

Modes

• Solo: the daily challenge is the same puzzle for everyone, at a level that depends on the day of the week (easy on Monday, formidable on Sunday). Take it on every day to lengthen your streak, then copy your result as one line of coloured squares, without giving away the answer. Free puzzles are endless, at the level of your choice.
• Against the AI: the same puzzle for both of you. The AI reasons out loud, scale after scale; the first to give the right total wins. A missed weighing freezes you for a few seconds.
• Two players: a deduction duel on the same device. Take turns announcing the weight of a hidden symbol (+10 if right, -5 if not) or the total of the final scale (+20 if right, -10 if not). A right total ends the game: whoever is ahead wins.
• Online: a race. The same puzzle for everyone, the fastest wins, penalties included.

Levels

• Easy: 3 symbols, weights up to 9. One scale after the other.
• Medium: 4 symbols, weights up to 12, symbols on both sides.
• Hard: 4 symbols, weights up to 15. You must combine two scales.
• Expert: 5 symbols, weights up to 18, two combinations to find.
• Devilish: 5 symbols, weights up to 20, big combinations and loaded pans.

About the AI

Every puzzle is built from randomly drawn weights, then checked by a solver that lists all the whole-number solutions: only one is ever left. A second solver reasons like a human (a scale with a single unknown, or a combination of two scales); it provides the hints and the AI’s reasoning. At low levels the AI hesitates and sometimes slips; at high levels it chains deductions without a mistake.