Unit 15 · Truth and Lie Logic
Cross-Country Race — Who Came First?
Lesson 1 of 2
Truth and Lie Logic questions give many students trouble — until they discover the universal method: assume one candidate is the answer, evaluate every statement in that world, and check whether any constraint is broken. Once this technique clicks, even the most confusing truth puzzle becomes a straightforward process of elimination.
Two-statement-per-person truth puzzles appear regularly in the medium difficulty band of OC TS. The "at most one false statement per person" constraint is a particularly powerful filter: a single double-false instantly eliminates an entire candidate without needing to check the rest.
The examiner is checking whether you can methodically test each possible winner, evaluate every statement under that assumption, count how many are false for each person, and identify which scenario produces no rule violations. The wrong answers are not random — each is eliminated by a specific contradiction.
Three people each make two statements about who won (or who is guilty). A rule limits how many of their statements can be false — typically "no more than one false statement per person per pair". Exactly one winner produces a consistent set of statement evaluations.
Best approach: Test each person as the winner, one at a time. For each test, go through every person's two statements, mark each true or false, and count the falses. If any person ends up with 2 false statements, that candidate is immediately ruled out — stop checking that test and move on. The candidate where everyone ends up with 0 or 1 false is the answer.
Question
Three students — Asha, Beau, and Cody — ran in a school cross-country race. Their teacher confirms that exactly one of the three finished in first place. Each student makes two statements about who came first. Some statements are true and some are false. However, no more than one statement in each student's pair is false.
| Asha | Beau | Cody |
|---|---|---|
| Beau came first. | I did not come first. | Asha came first. |
| Cody did not come first. | Cody came first. | I did not come first. |
Based on the given information, which one of the following statements must be true?
Select an answer to see the explanation.
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