Walking Ants

Jaadu mailed me this problem today. I was able to solve it and I am happy. This is an "intelligent" problem. Solution so elegant that you will fall in love with it. :)

Assume 100 ants are moving in 1 dimensional plane, all move with the same speed. Some are moving towards the positive x axis and some towards negative. If a collision occurs between two ants both ants changes the direction. If you are given direction of motion of each ant, what is the number of collision that will occur? Give an algorithm. :)

Update (11/12/09): Solution by A Rustle (Prathmesh, CSE, IITB) in comments !!

Comments

  1. A Rustle10:14 PM, October 11, 2009

    For an ant moving right, count the number of ants to its right moving left. Add this number for every right moving ant. That is the number of collisions.

    hint: on every collision, assume that the two ants don't change direction but simply cross each other.

    ReplyDelete
  2. Pratik Poddar11:12 PM, October 11, 2009

    @Rustle
    Great!! Correct!! Nice solution..

    ReplyDelete
  3. Gold and Iron12:22 PM, October 12, 2009

    nice solution good question

    ReplyDelete
  4. scadza6:25 PM, October 12, 2009

    Its a nice problem. i was thinking of writing about...(trying to cp u)

    ReplyDelete
  5. Pratik Poddar6:31 PM, October 12, 2009

    :)
    yo dharme!!

    ReplyDelete

Post a Comment

Popular posts from this blog

Buying Dimsums

Source: Alok Goyal (Stellaris VP, Ex-Helion VC) puzzle blog Problem: A fast food restaurant sells dimsums in boxes of 7 and 3. What’s the greatest number of dimsums a person cannot buy. Generalize it for p and q where p and q are relatively prime. I loved the puzzle. Hope you enjoy it too.
Read more

Fraction Brainteaser

Source: Sent to me by Gaurav Sinha Problem: Siddhant writes a Maths test and correctly answers 5 out of 6 Arithmetic questions and 20 out of 28 Geometry questions.  In total, Siddhant scores 25 out of 34.  Vaibhav writes another Maths test and correctly answers 20 out of 25 Arithmetic questions and 6 out of 9 Geometry questions. in total, Vaibhav scores 26 out of 34. Note that a) Vaibhav scores more than Siddhant b) Siddhant score better than Vaibhav in both individual topics -  5/6 > 20/25 and 20/28 > 6/9 How is it possible? 
Read more

Consecutive Heads

Let's say A keep tossing a fair coin, until he get 2 consecutive heads, define X to be the number of tosses for this process; B keep tossing another fair coin, until he get 3 consecutive heads, define Y to be the number of the tosses for this process. 1) Calculate P{X>Y} 2) What's the expected value of X 3) What's the expected value of Y This is probably the hardest puzzle I have ever put on my blog. Hence, I will post its solution in the post directly rather than on comment. Solution: 1) (Solved by me finally after 13 months :)) Make a state diagram. Let the state be (a,b) where a is the number of consecutive heads streak "A" is on currently and b is the number of consecutive heads streak "B" is on currently. So, (0,3) (1,3) are final accepted states and (2,0) (2,1) (2,2) (2,3) are failure states. If you get tails, your contribution to the state reaches to "0" f(State) = P(X>Y | "State" configuration initially) ...
Read more