Sunday, November 13, 2011

Fox and Duck Interview Puzzle

A number of different versions of the puzzle are available. For this post we are using the Fox and the Duck version. A duck, pursued by a fox, escapes to the center of a perfectly circular pond. The fox cannot swim, and the duck cannot take flight from the water. The fox is four times faster than the duck. Assuming the fox and duck pursue optimum strategies, is it possible for the duck to reach the edge of the pond and fly away without being eaten? If so, how?

From : IndiaDiscuss.com Interview Questions and Puzzles

Solution:
This is not a simple mathematical puzzle to solve like normal common problems. Fox in this puzzle is too fast and clever for any normal and simple strategy.

From the speed of the fox it is obvious that duck cannot simply swim to the opposite side of the fox to escape. Pi*R/4 < R.

Let V be the speed of Duck and 4V speed of fox.

Now we need to find out the position from where duck can swim to the shore in time less then Pi*R/4V. Pi = 3.14.

To keep things simple we will take the distance from center for the duck to escape when the fox is on the exact opposite side of the pond to be R/4.
So duck can swim in 3R/4V which is less than Pi*R/4V.

Now the next challenge is how we can make sure the clever fox will be on the opposite side. Here is the tricky part.

Let the duck rotate around the pond in a circle of radius R/4. Now fox and duck will take exact same time to make a full circle. Now reduce the radius the duck is circling by a very small amount (Delta). Now the Fox will lag behind, he cannot stay at a position as well. Now in due time duck will get to a position we wanted, 3/4*R distance away from shore where fox is on the exact opposite side of the pond. From there duck can swim safely to shore and fly away.

13 comments:

Unknown said...

It's nice blog and quite informative to help to know about much new things i was not knowing .
Can you tell me how we will create or can tell me Volume of a Sphere Formula .So will be used to calculate .

jaesmin100 said...

Thanks Sway, I like puzzle toddler puzzl,ebaby puzzle, this puzzle too as it needs logical thinking to be able to complete. Will you be trying this out on your pupils?

please follow this link

https://play.google.com/store/apps/details?id=com.woozle&hl=en_GB

Ashutosh Mukherjee said...
This comment has been removed by the author.
Ashutosh Mukherjee said...

elaborate this part a bit more...

To keep things simple we will take the distance from center for the duck to escape when the fox is on the exact opposite side of the pond to be R/4.

ahuman.life said...

So people who like to solve puzzles online visit martmind.com on facebook -- page developed by martmind.com(BUY - THINK -GET SUCCESS)

Thank You all

Unknown said...

More Interview Puzzles

Unknown said...
This comment has been removed by the author.
Globalias Academy said...


Best ias coaching in bangalore
.www.globalias.in

Nicole Bolton said...

There are many interesting information included and i can easily understand all given information.I post something on my blog to post something, or wait to post something worth saying. Keep update more information....
Logistics management software
Manufacturing ERP
Oil and gas ERP

Unknown said...

This is so informative blog and i have used this 5 minutes thing very useful too happy with this blog........
SAP FICO Training in Chennai

Unknown said...

this is very nice post and thanks for sharing this wonderful information!!!


SAP MM Training in Chennai

Globalias Academy said...

Best ias coaching in bangalore
.www.globalias.in

Unknown said...

Amazing Article ! I have bookmarked this article page as i received good information from this. All the best for the upcoming articles. I will be waiting for your new articles. Thank You ! Kindly Visit Us @ Coimbatore Travels | Ooty Travels | Coimbatore Airport Taxi | Coimbatore taxi | Coimbatore Taxi