What is the smallest number of ducks that can swim in a single straight line…
2010
What is the smallest number of ducks that can swim in a single straight line such that two ducks are in front of one duck, two ducks are behind one duck, and one duck is between two ducks?
Answer: D. 3 — ConceptWhen relative-position statements can refer to the same objects, the stated counts must not be added separately. Construct one arrangement, test every…
- A.
5
- B.
7
- C.
4
- D.
3
Attempted by 3 students.
Show answer & explanation
Correct answer: D
Concept
When relative-position statements can refer to the same objects, the stated counts must not be added separately.
Construct one arrangement, test every condition on it, and then prove that no smaller arrangement can satisfy all the conditions.
Application
Place three ducks in a straight line: a front duck, a middle duck, and a rear duck.
For the rear duck, the front and middle ducks are the two ducks in front of it.
For the front duck, the middle and rear ducks are the two ducks behind it.
The middle duck lies between the front and rear ducks.
Cross-check
Two ducks cannot work because no duck could then have two ducks in front of it or two ducks behind it. Thus three is both sufficient and minimal.
Therefore, the smallest number of ducks is 3.