Deterministic logic puzzles
How to Solve Clock-Offset Logic Puzzles
Choose one clock as the reference, translate every statement into a signed minute offset, and carry that offset through the chain before answering. If two paths reach the same clock, they must agree. Work from relationships rather than guessing the pictured time.
Clock-offset cases look visual, but the reliable solution is symbolic: one reference, signed minute differences, and a consistency check. The same facts always produce the same answer.
Reference
Anchor one clock before following the chain
Write the reference as zero. A clock stated to be 12 minutes fast becomes +12; one stated to be 7 minutes slow becomes -7. Keep the sign attached to the relationship.
Chain
Combine relationships one edge at a time
If B is 12 minutes fast relative to A and C is 5 minutes slow relative to B, then C is +7 relative to A. Do not compare pictured clock faces until the relationship chain is complete.
When a statement reverses direction, reverse the sign as well. Most wrong answers come from keeping the number but losing its direction.
Verify
Use a second path as a consistency check
A case may provide two ways to reach the same clock. Calculate both independently. Matching offsets support the chain; a mismatch shows where a direction or arithmetic error entered.
- Every relationship has a direction.
- Every minute value keeps its sign.
- Two paths to the same clock agree.
- The final answer follows from the offsets, not a visual guess.