A balance scale puzzle game uses three equal-pan weighings to identify one odd coin among twelve, and a complete five-round run awards exactly 1,000 points. Twelve numbered coins look identical, but exactly one is heavier or lighter than the rest, and the direction is not known in advance. You choose which coins to place on each pan, observe one of three possible results — left heavier, balanced, or right heavier — and after the third weighing name the numbered coin and mark it heavier or lighter. Each weighing rules out candidates in real time, so the strategy is to plan three comparisons whose combined three-result vector is unique for every one of the 24 possible hidden states. The full five-round run is reproducible: the hidden fixtures are coin 1 heavy, coin 6 light, coin 12 heavy, coin 8 light, and coin 10 heavy, in that order.
What the Balance Scale Puzzle Game Asks You to Do
The task is concrete and finite. You face twelve numbered coins that look the same to the eye, but exactly one coin has a different ideal weight, and the difference may be heavier or lighter. You do not know in advance which coin is odd, and you do not know which direction the difference runs. The only tool you have is an ideal equal-pan balance, and the only operations it supports are putting equal numbers of distinct coins on the left and right pans and reading one of three possible results.
You may run at most three weighings per round. After the third valid result, you must name both the numbered coin and whether it is heavier or lighter than the rest. A correct answer in a round adds 200 points and starts the next round. A wrong answer lets you retry within that round, but a second different wrong signature in the same round deadlocks the run until you press Restart. The Weigh now control stays unavailable until both pans contain the same positive number of distinct coins, so a mismatched pan count simply pauses the round.
How the 24-Case Strategy Fits in One Schedule
One odd coin among twelve, with two possible directions, gives 24 hypotheses: coin 1 heavy, coin 1 light, coin 2 heavy, coin 2 light, and so on through coin 12. Every weighing has three possible outcomes, so three weighings can in principle produce 27 distinct result sequences. That capacity is just barely enough to assign a unique sequence to each of the 24 states — but only if the three comparisons are chosen carefully. A naive schedule can give two different hypotheses the same sequence, which is why the balance scale puzzle game verifies every disclosed plan mechanically with an independent numeric oracle.
The disclosed schedule is non-adaptive and uses 4-versus-4 rows: each weighing places four distinct coins on the left and four on the right, leaving four coins off the scale. The same three rows work regardless of what the previous results showed, which is stronger than needing a different branch after every result. Each coin has a distinct three-position pattern across left pan, right pan, and off scale, and the same coin being heavy produces the opposite three-result vector from that same coin being light. The result is 24 unique vectors for 24 hypotheses, so after the third weighing the candidate count collapses to exactly one. The mathematical basis for the twelve-coin problem and its four-versus-four opening is documented by NRICH at the University of Cambridge, and Plus Maths independently explains the three possible balance outcomes and the twenty-four candidate states.
Play Through a Round: Build Pans, Weigh, Record
Follow these steps for each of the five rounds in the Coin Weighing Puzzle balance scale puzzle game.
- Open the round. The board shows twelve numbered coins and an empty equal-pan balance. The Weigh now control stays disabled until both pans hold the same positive number of distinct coins, so start by assigning at least one coin to each pan.
- Choose your first comparison. Either drag or click coins onto the left and right pans, matching pan counts, or press P (or click Load plan) to apply the next disclosed four-versus-four row from the schedule. The disclosed plan is the fastest path to one candidate.
- Press Weigh now. Read the three-state result: left pan heavier, pans balanced, or right pan heavier. The candidate counter drops from 24 by filtering out hypotheses that disagree with that result. The pan groups, result code, and remaining candidate count are recorded in the visible log, then the board clears for the next comparison.
- Run two more weighings. Repeat the build-and-weigh cycle twice more. After each weighing, candidates inconsistent with the observed outcome are removed. A fourth weighing is impossible; the answer controls appear only after three valid results.
- Name the odd coin and its direction. Select a numbered coin, mark it Heavier or Lighter, and submit. A correct guess adds 200 points and loads the next round. Repeating the same wrong coin and direction in the same round does not count twice, but a second different wrong guess deadlocks the run until Restart.
Five Fixed Rounds and the 1,000-Point Path
Every correct coin-and-direction identification awards exactly 200 points, and the route to the full 1,000-point finish is five rounds. The hidden fixtures are not randomized: round 1 is coin 1 heavy, round 2 is coin 6 light, round 3 is coin 12 heavy, round 4 is coin 8 light, and round 5 is coin 10 heavy. Because the fixtures are fixed, the complete route can be reproduced and audited by anyone who follows the disclosed 4-versus-4 schedule.
The same five fixtures also exercise different parts of the strategy. A heavy coin near the start of the numbering tests one corner of the schedule, a light coin in the middle tests another, and the round-5 odd coin sits at the edge of the table. Players who try their own pan groups can still finish the run, but an uninformative route may leave several candidates after three weighings, and the game still requires one final guess without adding an extra comparison.
Keyboard, Mouse, and Touch Controls Compared
| Action | Keyboard | Mouse / Pointer | Touch |
|---|---|---|---|
| Move selected coin | Arrow keys | Click coin, then click destination | Drag coin to pan |
| Send coin to left pan | A | Click left pan zone | Tap left pan |
| Send coin to right pan | D | Click right pan zone | Tap right pan |
| Remove coin from scale | X | Click off-scale area | Drag back to bench |
| Load disclosed plan row | P | Click Load plan | Tap Load plan |
| Weigh valid pans | Enter | Click Weigh now | Tap Weigh now |
| Select highlighted suspect | Space | Click numbered coin | Tap coin |
| Mark heavy or light | H / L | Click Heavier / Lighter | Tap toggle |
| Submit final answer | Enter | Click Submit | Tap Submit |
Every coin and action is a large button, so the same interface accepts pointer, touch, and physical keys without a separate mode. Before three weighings, the A/D/X/Enter set is live; after three weighings, the Space/H/L/Enter set takes over for the answer controls. A shared GameShell supplies score, optional locally stored best score, Restart, keyboard help, and a double-Escape boss key.
What the Game Does Not Model
The balance scale puzzle game is an idealized recreation, not a physical weighing application. It does not simulate calibration error, friction, manufacturing variation between otherwise normal coins, numerical mass, measurement uncertainty, damaged scales, or real currency values. The numeric 10, 11, and 9 values used by the independent development oracle exist only to make ideal pan sums easy to recompute; runtime gameplay uses only the declared heavy-or-light hypothesis and membership on equal pans.
The mathematical boundary is deliberate. Runtime gameplay stays on the declared hypothesis set, and no fourth weighing is granted even when the candidate count remains above one. No responses leave the browser, no account is required, no gameplay API is called, and no external asset or new package is loaded, so the puzzle stays a self-contained logic exercise from start to finish.
Strategy Tips That Generalize Beyond Round 5
Once you understand the non-adaptive 4-versus-4 schedule, a few habits transfer to any custom route. Always keep the pans equal in count, because unequal pans leave Weigh now disabled and waste a comparison. Treat each result as evidence rather than decoration: the candidate counter is filtered from the actual observed outcomes, and a single uninformative weighing can leave you with several candidates at the end. If you go off-script, plan to assign a unique three-position pattern to each coin so the vectors separate cleanly.
Following the disclosed plan ends with one candidate after the third result for every possible odd coin and direction, which is why the plan is the fastest path to the 1,000-point finish. A useful companion is the 12 Coins Puzzle guide, which walks through the same three-weighing strategy from the puzzle-history angle.