Move to the North

An interesting quant puzzle asked in an placement interview at Quadeye

How many points are there on the globe, so that if you walk 1km south, then 1km east and then 1km north, you reach the place where you started

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Try to solve this problem yourself before moving on to the solution below

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Solution

The North Pole is a clear answer. If a person is at the North Pole and moves 1km South, then 1km East, and then 1 km North, he will reach the North Pole again.

Now consider latitudes on the globe. They have different circumferences ranging from max at the equator to 0 at the poles. There will be one ring a little above the south pole with a circumference equal to 1. So take any point on the latitude 1 km north of that ring. If you start from any point and move 1 km south, you will reach the latitude with circumference 1; moving 1 km east or west will get you to the same point. Now moving 1 km north will take you to the original starting point.

Some guys also argue for all the points 1km above the South Pole as East is not defined at the South Pole. So, you can’t move anywhere and moving 1km north will get you to the starting point but that’s just playing on the definition. You might mention this to show a little creativity.

😃 Over to you: Were you able to solve this?

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