Discussion
An ant is at the bottom-left corner of a grid (point P) as shown above. It aims to move to the top-right corner of the grid. The ant moves only along the lines marked in the grid such that the current distance to the top-right corner strictly decreases.
Which one of the following is a part of a possible trajectory of the ant during the movement?
- A.
- B.
- C.
- D.
Answer: C
The possible trajectory is (C).
The ant starts at the bottom-left corner and the target is the top-right corner, which is up and to the right. A step up or a step to the right along a grid line moves it closer to that corner, while a step down or to the left moves it away. So every allowed path is a staircase made only of up and right moves.
Path (C) goes up, right, up, right, so its distance to the target keeps falling. Path (A) ends with a step down, and path (B) also turns down after its last move right, so the distance grows on those steps. Path (D) is a closed loop that returns to P, which must include moves down and left.
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