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Grid path (turn-left puzzle): Find the initial northward distance from the start. A boy cycles north, then turns left and rides 1 km (west), then turns left again and rides 2 km (south). He ends up exactly 1 km west of his starting point. How far did he ride northward initially?

Q: Grid path (turn-left puzzle): Find the initial northward distance from the start. A boy cycles north, then turns left and rides 1 km (west), then turns left again and rides 2 km (south). He ends up exactly 1 km west of his starting point. How far d…

Given data & coordinates Start S = (0,0)Go north = x km ⇒ (0, x)Left to west 1 km ⇒ (−1, x)Left from west ⇒ south 2 km ⇒ (−1, x − 2)End is 1 km west of S ⇒ y must be 0 ⇒ x − 2 = 0 ⇒ x = 2. Final Answer 2 km

Difficulty: Easy

1 km
2 km
3 km
5 km

Correct Answer: 2 km

Explanation:

Given data & coordinates
Start S = (0,0)Go north = x km ⇒ (0, x)Left to west 1 km ⇒ (−1, x)Left from west ⇒ south 2 km ⇒ (−1, x − 2)End is 1 km west of S ⇒ y must be 0 ⇒ x − 2 = 0 ⇒ x = 2.

Final Answer
2 km

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