On Friday I posted this puzzle…..

My friend left her house, walked 5 miles south, turned east and walked another 5 miles, turned north and walked another 5 miles, and arrived back home.  Where does she live?
If you have not tried to solve it, have a go now.  For everyone else, the answer is after the break.
One answer is that she lives at the North Pole.  But there are other answers…. what did you think?
I have produced an ebook containing 101 of the previous Friday Puzzles! It is called PUZZLED and is available for the Kindle (UK here and USA here) and on the iBookstore (UK here in the USA here). You can try 101 of the puzzles for free here.

1. Roar Johnsen says:

Any point just over 5 miles from the south pole, – walking towards the south, in a cicle around the point and back north will do.

1. Anonymous says:

didn’t think of that, nice one

2. I think this wouldn’t work, because when you reach south pole, you can’t turn east – the only way from the south pole is north.

3. Eugenia,

That’s why you start just *over* 5 miles from the south pole. You don’t reach the pole itself; instead, you walk around it in a circle with a circumference of 5 miles.

4. MaciejK says:

A circle with circumference equal to 5 has the radius of about 0.8. So to be precise any point 5.8 miles from the south pole will do.

5. ChrisR says:

MaciejK, I think that it is almost impossible to be *precise* about anything which involves pi 🙂

2. ChrisR says:

or twice round, or three times round…
Lateral thinking leads to circular argument!

3. Charlotte says:

How is it the North Pole?

1. Very chilly.

2. Charlotte: Think about it. You walk south from the north pole (which is any direction–on the north pole all directions are south!) for 5 miles. Now you walk east 5 miles. This means you’re walking in a circle keeping the north pole on your left, but maintaining your 5-mile distance. It doesn’t matter how far east you go, you’re still exactly 5 miles away from the pole. Now you turn and go north again for 5 miles, and you’re back at the pole!

Most people don’t stop to consider that east and west are really circular paths–the circles are smaller and smaller as you get near the poles. Your whole trip forms the shape of a slice of pie.

4. Jethro says:

I remember a similar puzzle from my childhood. During the journey described the person encounters and shoots a bear – the question posed was ‘what colour was the bear’

1. Stevenz says:

Well?

5. ctj says:

1. north pole
2. near the south pole. stated precisely, her house is 5+5/(2pi*n) miles from the south pole, where n is the number of times she walks around the pole.
3. her house is on the north pole of phobos, where the pole is roughly 5 miles from the equator.

1. I very much like that 5 + 5/(2pi*n) answer. For very large n one would get quite dizzy. That’s why I gave the “getting dizzy” clue on Friday.

2. Is it *precisely* 5+5/(2pi*n) though because we are on a curved not flat surface?

6. Bo Murugend says:

A small correction.

If you turn and walk east, you would actually not stay on the same latitude(because of the curvature of the surface), and would therefore have to walk further than 5 miles northwards to get back home.

You could fix this if you kept looking at the compass while corrected for the curvature deviation while walking eastward.

An alternative answer would be that you live on a tiny planet where the distance from the poles to the equator is exactly 5 miles. Turning and walking eastward would here ensure that you stayed on the equator, and therefore 5 miles from the north pole.

Interestingly, the path you walk on would trace a triangle with three 90-deg angles.

1. One Eyed Jack says:

So long as we’re picking nits, a planet with a circumference of 20 miles would be too small to be a planet and too small to generate magnetic poles.

2. Toni says:

How do you mean? If you reference true north and turn to the east you would indeed follow the same latitude. With the logic you describe you could not complete a circle around the globe on the same latitude. However, It will not be a great circle track.

3. Bo Murugend says:

What I meant is that you can not follow the same latitude by walking in a straight line, unless the latitude is the equator, a great circle. Walking eastward along a latitudinal circle would require you to constantly turn slightly to the left(as long as you are in the northern hemissphere).

This effect is more pronounced the closer you are to the poles. So when you are only 5 miles from the pole, the discrepancy between the latitudinal circle and a straight line, which would be a tangent to the circle, is considerable.

If however you continuously look at the compass and correct for the discrepancy, you could track the globe on the same latitude. This is however, not the same as turning east and walking in a straight line.

4. ChrisR says:

Point taken, and it is an interesting one, but ‘walk in a straight line’ is not in the question

5. I think the wording of the problem is just a bit flawed. It does not say “walked east for five miles.” What it actually says is “turned east and walked another 5 miles”. These two versions put her in two different places.

7. Some more explanations:
– Her house was 5 miles wide.
– Her house was on a 5 mile wide block of land, all of which was her “home”.
– She uses the term “home” to refer to her family home (i.e. where she grew up). So she left her “house” and then returned to her “home”.
– She’s a Paul Young Fan, and took her hat with her.

8. NickC says:

Any place with a gym located 5 miles south of her home with an east facing treadmill

9. kaggyx says:

She lives on the tip of a ballpoint.

10. Anonymous says:

On top a matchstick.

11. Anonymous says:

On top of a matchstick

12. Per says:

She lives in a mobile home that is driven by someone else very slowly (1/3 of walking speed) eastward at the same time.

13. What I would do is to put the map projection onto a 1/8 sphere. Three 90 degree angles and you’re back where you started

14. John says:

I said that she might live in a gym with some treadmills.

15. N says:

she lives in the same house from where she left

16. Jeff says:

5 plus 2.5 divided by pi from the South Pole, 5.79577471546 miles from the South Pole. So an ∞ number of places.

17. Henry says:

At least where I live there are plenty of roads labeled “south” that really travel south by southeast, and roads labeled “east” that really travel east by northeast, so if your friend were going by the road labels rather than her compass, she could live a lot of places far less exotic than the North Pole.

18. sai gpv says:

The Bus Conductor !

Once there was a bus conductor, who was very rude to his passengers.

One day a beautiful young girl, of around 18 years,tried to board the bus, but he didn’t stop the bus Unfortunately the beautiful young girl came under the bus and died on the spot.

Angry passengers took the conductor to the police station, who in turn took him to the court.

The judge was not at all impressed with him and gave him capital punishment. He was taken to the electrocution chamber.

There was a single chair in the center of the room and a single banana peel at one corner of the room. The conductor was strapped to the chair and high voltage current was given to him. But to everyone’s amazement, he survived. The judge decided to set him free, and he returned to his profession.

After a few months, this time, a good looking middle aged woman tried to board the bus but the conductor didn’t stop the bus. Unfortunately, this time also, the good looking middle aged woman came under the bus and died on the spot.

Again angry passengers took him to the police station, who in turn took him to the court. The judge took one look at the conductor and gave him capital punishment. The Bus conductor was taken to the same electrocution chamber where there was a single chair in the center of the room and a single banana peel at one corner of the room. He was strapped to the chair and high voltage current was given to him. This time also, to everyone’s amazement, he survived. The judge decided to set him free, and he returned to his profession.

A couple of months later, an elderly gentleman tried to board the bus.

This time the Bus conductor, remembering his earlier experiences, stopped the bus. Unfortunately the elderly gentleman slipped and died due to his injuries. The conductor was taken to the police station and then to the court, to the same judge. Though he hadn’t done anything wrong, but considering his past record the judge decided to set an example and gave him capital punishment.

The Bus conductor was again taken to the same electrocution chamber where there was a single chair in the center of the room and a single banana peel at one corner of the room. He was strapped to the chair and high voltage current was given to him.

This time he died instantly !!!!!!!!!!!

The question is why didn’t he die on the first two occasions, but died instantly the third time??

Try to solve it yourselves. This is rather interesting and answer is perfectly logical. If necessary read the puzzle once again.

1. ChrisR says:

(apart from the fact it is the driver who stops the bus…) – do I spoil the fun of everyone else by giving the answer?
No, I’ll just say I know it.

3. The answer I found by googling was the part I’d already figured out. But what’s with the banana peel???

and isn’t the primary answer actually backwards? (trying to remain cryptic so as not to spoil)

4. Anne Elk says:

Rod: I’m also going to try not to spoil anything, but assuming we’ve got the same answer, it’s not backwards; it does work. I spent a few minutes working on increasingly desperate plays on the words “a peel” (i.e. “appeal”). I know it’s a bobbins joke but I wasn’t clever enough to find the right answer, so I Googled on its ass… as it were.

19. Anne Elk says:

Two puzzles for the price of one this week! I got the North Pole one easily enough but I had to Google the bus conductor one. (I didn’t know how long I’d have to wait for the answer.) I laughed out loud at the answer. Nice one, sai gpv!

20. Todd says:

A houseboat that floats easterly down a canal/stream exactly five miles in the time that it take you to make your 15 mile journey.

21. Tim says:

She is homeless 😛

22. Darren h says:

Assumed it would be north pole even though i am too much of a moron to e able to wrk out why

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