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## Question

Here's another one from Math Magic.

A man has breakfast at his camp. He gets up and travels due North.

After going 10 miles in a straight line he stops for lunch. After lunch he gets up and travels due North. After going 10 miles in a straight line he finds

himself back at camp. Where on earth could he be?

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When you say "travels due North".

Do you mean using a compass or adapting with the sun's position???

He would be at one of the poles during the 6 months of sun shine...

If he assumes that after lunch, the sun is pointing to West...

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on the north pole ...

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Here is my solution

He could be at any point(infinite possibilities) that is 5 miles south from north pole

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Here is my solution

He could be at any point(infinite possibilities) that is 5 miles south from north pole

I believe you're right.

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Here's another one from Math Magic.

A man has breakfast at his camp. He gets up and travels due North.

After going 10 miles in a straight line he stops for lunch. After lunch he gets up and travels due North. After going 10 miles in a straight line he finds

himself back at camp. Where on earth could he be?

5 miles south of the North Pole

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Here's another one from Math Magic.

A man has breakfast at his camp. He gets up and travels due North.

After going 10 miles in a straight line he stops for lunch. After lunch he gets up and travels due North. After going 10 miles in a straight line he finds

himself back at camp. Where on earth could he be?

Could he not be 10 miles from the South Pole?

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Could he not be 10 miles from the South Pole?

Nah, he'd end up 30 miles from the South Pole if he went North twice.

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Is the person constantly traveling North or does he find North once and then walk for 10 miles? If he is constantly going North, which is how I read this, then I can't make sense out of it. I believe the answer is meant to be the North Pole, but at some point in his travels he is not traveling North.

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Is the person constantly traveling North or does he find North once and then walk for 10 miles? If he is constantly going North, which is how I read this, then I can't make sense out of it. I believe the answer is meant to be the North Pole, but at some point in his travels he is not traveling North.

Yeah, I think he looks at his compass, and heads north for ten miles, even though 5 miles into it he's traveling south. You can't travel north from the north pole. The 5 miles south of the North pole answer works.

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Here's another one from Math Magic.

A man has breakfast at his camp. He gets up and travels due North.

After going 10 miles in a straight line he stops for lunch. After lunch he gets up and travels due North. After going 10 miles in a straight line he finds

himself back at camp. Where on earth could he be?

... five miles from the North Pole

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nice discussion for this one is here as well

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I don't think the answer is limited to being five miles from the North Pole.

The man could be anywhere that is less than 10 miles from the North Pole, except for actually being at the North Pole itself.

As long as he is within 10 miles of the North Pole, and not actually at the North Pole, then if he travels by heading due North, he will at some point pass the North Pole. Thus beginning his second journey by heading due North will take him in the exact opposite direction and back to his camp. If he began at the North Pole, he could not travel North, because from his perspective any direction would be South. For the same reason, he could not begin exactly 10 miles away from the North Pole, because then after stopping for lunch, from his perspective, any direction would be South once again. Starting any distance from the North Pole which is less than 10 miles, however, would work out fine. For obvious reasons, starting any distance further than 10 miles from the North Pole would not work.

If there is a reason why it would be limited to just five miles, please let me know.

Edited by zdr

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I don't think the answer is limited to being five miles from the North Pole.

Nice one zdr I wonder what the mental process is that causes most people to divide the distance in half

Infinite original locations < 10 miles from the North Pole

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Nice one zdr I wonder what the mental process is that causes most people to divide the distance in half

Thanks. I was wondering about the division in half tendency people have as well, as I tend to do that sort of thing myself and started to avoid it from past experience. I think it might be because just about everything else from the two journeys is the same, so it seems to fit that it would work that way. It's strange how often people tend to do it though.

Edited by zdr

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The question states he started travelling due North for ten miles in a straight line , it does not say he travelled North ten miles.

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5 miles sth of nth pole

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i am too quick, less than ten miles from the nth pole works too i think

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i am too quick, less than ten miles from the nth pole works too i think

Yes it does, but the question implied a common denominator for both the base camp and the rest camp -"where on earth am I ?" - albeit not a specific point, but a common location, that location would be the parallel of latitude -Base camp where am I?...Rest camp where am I? 89º 55.0´N.

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