Problem 20 · 2015 Math Kangaroo
Medium
Logic & Word Problems
casework
The teacher asks five of her students how many of them had studied the previous day. Azra says: “Nobody.” Berti says: “Only one.” Christa says: “Exactly two.” Doris says: “Exactly three.” Emina says: “Exactly four.” The teacher knows that students always lie if they haven’t studied and are always truthful when they have studied. How many of those students had studied the previous day?
Show answer
Answer: B — 1
Show hints
Hint 1 of 2
The five claims 0, 1, 2, 3, 4 are all different, so at most one of them is true.
Still stuck? Show hint 2 →
Hint 2 of 2
A student tells the truth exactly when they studied, so the number who studied equals the number of true statements.
Show solution
Approach: find the count that makes exactly the truth-tellers truthful
- Students who studied tell the truth; the others lie. So the number who studied equals the number of true statements.
- The five statements give five different counts, so at most one is true, meaning at most one student studied.
- If exactly one studied, that student truthfully said 'Only one' and the other four lie - which is consistent.
- So 1 (B) student had studied.
Mark:
· log in to save