# Classic Puzzles

## Wednesday, December 27, 2006

### Microsoft Interview Question : Polar Bear

One of the most asked and well known microsoft interview question is that of the walking bear.The question is still asked because a lot of people have either not heard of it or most of them don't know the correct solution yet.

If a bear walks one mile south, turns left and walks one mile to the east and then turns left again and walks one mile north and arrives at its original position, what is the color of the bear.

Well,from the very framing of the question it is evident that we r talking about the poles,and all polar bears are white.You can also very well argue that any bear or man walking the same path will reach the same starting position if he is at north
pole.The question can also be extended and that's what we are interested in.

The question is how many such points exists on the surface of the globe.
Well,whats your answer,is it one or infinity

#### 29 comments:

Jim Miles said...

Infinity.

There is indeed the one point exactly on the north pole where walking 1 mile south, 1 mile east then 1 mile north returns you to the starting position but there is also a circle of infinity points in the southern hemisphere.

Let us call this circle 'A'. It is formed by the points 1 mile north of another circle 'B' of circumference 1, parallel to the equator and between the equator and the south pole.

Suppose you are on 'A'. Then going 1 mile south puts you on 'B'. Travelling 1 mile east lands you up exactly where you just were on the circle (because the circumference of 'B' is 1). Then travelling north puts you back where you started.

However, 'A' is not the only circle of such points. In the same way that we constructed 'A' by taking the points 1 mile north of the circle 'B' of circumference 1, parallel to the equator, between the equator and the south pole we may take any circle 'A_n' of points 1 mile north of the circle 'B_n' of circumference 1/n (for any n in the natural numbers), parallel to the equator, between the equator and the south pole.

Think about it! :)

Suman said...

Thats a good question and i agree with jim miles solution.

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hugo bowne-anderson said...

great, jim.

so: as your n gets really, really big, the circle B_n gets closer and closer to the south pole.

so in the limit as n goes to infinity, we find another solution!, which is:

start at any point on the circle A' which is all points 1mile north of the south pole.

then when you get to the south pole, walking east is doing nothing!

Narendran Kumaragurunathan said...

The bear is white because, there are no bears on south pole.

Eighth Wonder said...

There r no polar bears in Antarctica.
Answer is north pole,which is exactly a point on earth.

Thiep said...

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I just came across your blog and wanted to drop you a note telling you how impressed I was with the information you have posted here.

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Source: Microsoft interview questions

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aashish said...

To add: Somebody might think that such a circle (of unit circumference) can exist in northern hemisphere also all the points lying on circle one mile above(the circle of unit radius) will also be the answer but it is not possible because the distance of north pole from this circle would be 1/2*pi which is less than 1 so only one point in northern hemisphere and i.e north pole.

aashish said...

ohhhh sry instead of radius it should be circumference at one place

Lily said...

My husband became like a polar bear he is like an iceberg with me so I had to suggest him Viagra Online because I just need to be with my old sweetheart husband.

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guddu said...

infinity...as we earth is as a hemisphere so we cannot say there is one point.

lavesh said...

Hi I got inspired by your blog and created my own puzzle blog
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Lauraine said...

That bear should be white. Bcoz it started one mile south from north. So it lives in north. That's it should been white.
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Chankey Pathak said...

Color: White (North pole's bear are white and also there are no bears in south pole)

sophia-yang said...

AT THE FIRST SIGHT IF THIS ARTICLE, I THINK OF A SONG POLAR BEAR OUR FOREIGN TEACHER TOUGHT US EVER. IT IS A SO WARM MEMORY FOR ME NOW!
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Rajesh said...

excellent solution given by Jim!
Hats off..

Ashutosh Mukherjee said...

but y do we consider that bear statred off from north pole...not obviously soth but it can be any place and then how do we come to the conclusion

Ashutosh Mukherjee said...

and how do we arrive at this...

we may take any circle 'A_n' of points 1 mile north of the circle 'B_n' of circumference 1/n (for any n in the natural numbers), parallel to the equator, between the equator and the south pole.

Ian Webb said...

It would be very difficult to find any bears at the Magnetic North Pole, considering it is in the middle of the sea!

Prashant Gadkari said...

Amazing solution, Jim ! Just out of curiosity, how much distance south would one need to travel to reach the South Pole from the Circle B ( with a 1 mile circumference) ?

Prashant Gadkari said...

Amazing solution, Jim ! Just out of curiosity, how much distance south would one need to travel to reach the South Pole from the Circle B ( with a 1 mile circumference) ?

Prashant Gadkari said...

Amazing solution, Jim ! Just out of curiosity, how much distance south would one need to travel to reach the South Pole from the Circle B ( with a 1 mile circumference) ?

Prashant Gadkari said...

Amazing solution, Jim ! Just out of curiosity, how much distance south would one need to travel to reach the South Pole from the Circle B ( with a 1 mile circumference) ?

Prashant Gadkari said...

Amazing solution, Jim ! Just out of curiosity, how much distance south would one need to travel to reach the South Pole from the Circle B ( with a 1 mile circumference) ?

Realmatri.com said...

You are on north pole, it can’t be south pole because being at south, you can’t go south.

Read more

Eldhose Baby said...
HemanT AgrawaL said...

Nice puzzle.. my puzzle collection is here...

Top Logical Puzzles

Unknown said...

There is one more point , barring that vicinity circle concept, where in with these three movements you will come to original point??Wait for ans

Unknown said...

There is one more point , barring that vicinity circle concept, where in with these three movements you will come to original point??Wait for ans