Round & Revel / Unknown-weight inference

Balance Bureau

The pans remember the comparison, even when the labels lost their numbers.

2–6 players cooperating; no non-playing hostEstimated 20–35 minutes for three challenges; not live-playtested

Original authored print-and-play game. Time is a planning estimate; this edition has not had a live group playtest.

Good for: A patient puzzle group that enjoys turning comparisons into small deductions.

What you need

Practice BB00 and eight balance-record cards
One A–D deduction sheet per challenge, pencils, and scrap paper
Separate covered answer guide; a calculator is welcome

How to play

Restore four missing weights

A fictional weighing office has kept reliable records of several pan comparisons. Package types A, B, C, and D have lost their weight labels. Each type weighs a whole number from 1 through 7 units, inclusive. Find all four values. Different types are allowed to weigh the same amount. Every copy of one type has the same weight, and every printed balance record is accurate.

Read the pan notation

Each record lists the contents of its LEFT and RIGHT pans. A + A means two separate packages of type A, so it contributes twice A’s weight. “3 units” means known reference weight worth exactly 3, not a fifth unknown package type. Add every listed item on a pan. An equals sign means identical totals; LEFT HEAVIER means the left total is strictly greater; RIGHT HEAVIER means it is strictly smaller.

Prepare a shared investigation

Set BB00 aside for practice, choose three different challenge cards BB01–BB08, and cover the answers. Draw four rows labelled A, B, C, and D, each with candidates 1–7. Leave space for complete trial tuples in A/B/C/D order. Choose a first investigator and continue clockwise between puzzles. Nothing is hidden from a player: all pan records and all allowed values remain visible throughout.

Contribute one checkable step

On a turn, offer one observation, elimination, trial value, or complete candidate, or pass. Explain which printed record supports it. The next player checks the arithmetic or asks for clarification. Everyone may join the discussion, and nobody must work mentally. A calculator, scrap equations, and repeated aloud readings are welcome. The purpose of taking turns is to give every person a role in the reasoning, not to forbid collaborative thought.

Use the small range carefully

Remember that all four values are integers from 1 to 7 and may repeat. A strict comparison excludes equality. For example, A + A heavier than B does not mean A itself is heavier than B. A sum of two different package types has no special rule beyond addition. Avoid importing physical assumptions about package size, colour, density, or shape; those are not printed evidence.

Test whole candidates

You may freely revise trial values before submission. For a complete candidate, calculate each left total and each right total, then check that the result matches the recorded comparison. A candidate satisfying most records is still incomplete evidence. Cross out a value only when a reason rules it out, and restore it if the reasoning proves mistaken. All supplied cards have one complete four-number solution, but an individual record usually allows many possibilities.

Lock four labels together

When the group has values for A, B, C, and D, read them in that fixed order. Invite every player to verify a record or flag an unresolved question. Write the four final numbers clearly and say “lock” before opening the key. Do not replace a value after seeing the answer. Record numbers rather than vague rankings: knowing that A is heavier than B is not yet a restored weight label.

Score and continue

Earn 1 shared point if at least three of the four submitted weights are correct. Earn a second point if all four are correct. Two or fewer correct values earn 0. A blank value is incorrect, and an out-of-range value is incorrect even if a later calculation happens to fit. Play three cards for up to 6 points. There are no individual winners, speed bonuses, or tiebreakers. After scoring, use the pan totals in the key to understand a missed deduction.

Keep the records accessible

These are paper records; you do not need an actual scale, objects of measured mass, or any physical balancing. Read LEFT and RIGHT relative to the printed table, regardless of where players sit. Enlarge the cards or nominate a scribe if useful. Correct a copying error before submission without penalty. If a record is unreadable in a damaged print, replace the card instead of inventing its sign. Unseen cards provide later sessions; known answers can be used for unscored explanations.

A worked example

For practice BB00, the restored weights are A=5, B=5, C=6, D=3. The left/right totals in printed record order are 12 = 12; 8 = 8; 10 < 11; 11 = 11; 17 = 17. Every comparison agrees with the card, and every weight is in the allowed range. All four correct labels would score 2 points; exactly three correct labels would score 1.

Printable materials

Print one copy of the balance files and a candidate sheet for each selected challenge, or copy the four rows onto scrap paper. Keep the solution guide separate. Cards need no cutting and all comparison labels work in black and white.

BB00