Answers to Interesting Questions
>> Sunday, May 04, 2008
Here are the answers to "Interesting Questions", I posted earlier.
1. Imagine you were standing on South pole. Whichever direction you chose to go, it will be north. Travel one mile north. Then go 1 mile east. You will be traveling in a circular path, centering the south pole. Then when you come back south 1 mile, you will be on the south pole once again. Your path will be like a pizza piece. Ok, we have one. What else?
Time to goto North pole ....... What ??? Yeah, you will get infinite points like this.
Stand 1+(1/(2*pi)) miles away from the north pole. Now travel 1 mile north (you will be traveling towards north pole). Then go 1 mile east (you will be going exactly one mile around the north pole). then when you go 1 mile south, you will come back to the same location you started. We selected the distance so that, when we go one mile east, you will be going in a circular path around the north pole and you will go exactly one time around north pole.
There will be infinite number of points like this, which will be on a circle with radius = 1 + (1/(2*pi)) miles and making north pole the center. So do we have more?? Yes !!
How about going around the north pole twice to make that 1 mile. So you will start 1 + 1/(2*2*pi) away from the pole. Like this you can start at any of 1 + 1/(2*n*pi) points from the pole, which will be again infinite combinations.
So you will have infinity * infinity points to fulfill this requirement.
2. This is again tricky :). This is how you do this. You switch on any of the three switches, for about 10 minutes. Then switch it off. Then switch on, one of the other two. Its the time to go to the room now.
If the light is on, then what you have set just now is the switch.
If the light is off, touch the light.
If it is hot, then the switch is what you switched on first. The bulb is hot as it was on for 10 minutes (that is the trick).
If it is not hot, then it is the switch which you never touched.
3. This is completely based on assumptions.
Assume you have 3 windows in an apartment and there are 20 houses in an apartment complex. Assume we have 3 apartment complexes in a block and there are about 200 blocks in your city.
Summing all these info together, we will have about
3 windows/house * 20 houses/complex * 3 apartment complexes/block * 200 blocks/city = 36000 windows/city.
Let's say you want to earn $20 per hour and you can clean 2 windows/hour. Then to clean all the windows you will charge (36000 windows/city) * ($20 per hour/ 2 windows/hour) = $36000 * 10
4. There are different ways of doing this. The one I think the best is to use a ship. Mark the water level on the body of the ship first. Then put boeing 747 of whatever object, that you want to weigh on the ship. Get the difference in water levels and use Archimedes' principles to get the weight.
Will post answers to the next two later.
3 comments:
oh well - I can think of weighing the Boeing with a lever scale (the ones that you find with small balancing weights in the gym). Obviously the one in the gym is not right for the job (:)) but you can use the same principal to build a large enough scale to weigh the Boeing. I suppose you can even build three (smaller) scales that the plane can stand on (not a huge one that fits the whole plane)
There are large scales in truck weighing stations (ones you will see near highways) (see http://www.massload.com/weighing.htm) . AFAIK most of the new ones use ultra sensitive strain/compression sensors to electronically get the reading. I suppose you can go that route too if you want to weigh the Boeing :)
BTW I used to enjoy a book called 'Ganitha Vinodaya' (Fun with Math) which was translated from Russian. I suppose they have a English translation as well but I've no clue about the original author or the original name of that book. There are number of fun and interesting questions like this there. In fact I remember there was one question related to the earths curvature as well.
Ajith,
This is a good suggestion. But these are some interview questions which require practical answers. Meaning they should be doable *NOW*.
Yes you can use a scale, but are there are scales like that accessible. Anyway, good suggestions.
of course there are. These scales are available now (and if you see the site you'll see they even weigh these mining trucks. One loaded mining truck is as much heavy as a Boeing. The truck scales I mentioned can be found across many weighing stations across US)and I don't suppose they actually put the Plane on a ship to see how much it weighs ! As far as the scale technology goes I am convinced that there are scales that can weigh the plane (at least three scales that can keep the three points the plane hits the ground)
Another thing I came up with (after a Googling) is that you can use the acceleration to get the mass (weight) since most of the time the thrust of the engines is known. See this .
BTW I know the employer who asks such questions ;). May be you should revisit some of the old algo stuff as well since I've heard they are pretty big on that kind of stuff too.
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