Binary Logic & Matching

Binary Logic & Matching

Binary-logic sets hand you a few entities and a web of yes/no facts — who holds which job, who is telling the truth, who tapped what — and ask you to pin every value from clues that each rule out possibilities. Nothing is numeric; everything is deduction. The winning move is to turn the clues into a grid or a table of eliminations and let "exactly one per row, exactly one per column" do the work.

The matching grid (who does what)

When each of N people maps one-to-one onto N attributes (a role, a rank, a colour, a floor), draw an N x N grid and reason in eliminations:

1. One dimension per axis. People down the side, attributes across the top. If there are three dimensions (person / job / city), use one grid per pair and keep them consistent.
2. Enter direct clues as X or ✓. "Rehan is not the Analyst" is an X; "Mira is the Planner" is a ✓ — and a ✓ immediately X-es out the rest of that row and that column.
3. Force the singletons. If a column has X in every cell but one, that last cell is a ✓. Alternate between rows and columns until nothing new appears.
4. Chain relative clues. "The Analyst ranks better than Pia" means Pia is not the Analyst, and the Analyst's rank is strictly above Pia's — combine the two grids.

Truth-tellers, liars and responses

A second family fixes each statement's truth value instead of a matching. Everyone is a truth-teller or a liar (or, in response puzzles, each answer is one of a fixed menu — Yes / No / Maybe, one tap / two taps / three taps).

• Assume and test. Suppose person A is a truth-teller; follow the chain of forced consequences; if it contradicts a clue, A is a liar. With few people you can enumerate every truth-assignment and keep only the consistent ones.
• Count the totals. When responses carry values (1/2/3 taps), the aggregate — "the four answers summed to 8" — is itself a clue that eliminates assignments.
• Cross-reference. "Exactly one of B and C is lying" links two unknowns; such parity clues collapse the branches fast.

Common traps

• Treating "at least one" as "exactly one," or a one-directional clue ("A ranks above B") as if it fixed both positions.
• Stopping at the first consistent solution when a second exists — always ask whether the grid is forced or merely possible.
• Forgetting that a ✓ eliminates a whole row and a whole column, not just one cell.