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Recent content by pratikpoddar

  1. pratikpoddar

    Modified Huffman Encoding

    Problem: A telegraph machine can transmit only lines and dots; it takes 2 seconds to transmit a line, but only 1 second to transmit a dot. We generally want to transmit texts containing letters of the English alphabet, and digits (so we have N<=36 symbols in total). Therefore, a prefix-free...
  2. pratikpoddar

    Dwarf problem

    Solution as posted on http://pratikpoddarcse.blogspot.in/2012/11/math-olympiad-problem-simple-and.html Since the final state matches the initial state, we can imagine this process going on continuously. Consider the dwarf whose cup contains the smallest amount of milk just before he begins...
  3. pratikpoddar

    Ants on circle

    Very interesting problem. When two ants A and B meet, they change directions. Lets view this as when two ants A and B meet, they continue in the same direction but their "original point" gets changed by the reflection property by the radius at the point of intersection as the mirror. Now...
  4. pratikpoddar

    Pairwise Product Set Cardinality

    Source: Nick's Mathematical Puzzles Problem:Let n be a positive integer, and let \(S_n = {n^2 + 1, n^2 + 2, ... , (n + 1)^2}\). Find, in terms of n, the cardinality of the set of pairwise products of distinct elements of \(S_n\) For example, \(S_2 = {5, 6, 7, 8, 9},\) 5 × 6 = 6 × 5 = 30, 5 × 7...
  5. pratikpoddar

    Interview question

    Very interesting problem. Thank You. Interesting discussion on the blog: http://pratikpoddarcse.blogspot.com/2012/01/lazy-walking-strategy-puzzle.html
  6. pratikpoddar

    Russian Roulette (Difficult Version)

    solutions anyone?
  7. pratikpoddar

    Veit Elser’s Formidable 14

    Thanks AlexandreB
  8. pratikpoddar

    Veit Elser’s Formidable 14

    This is another of those problems I have not been able to solve since over an year. Fit disks of the following diameters into a circular cavity of size 12.000: 2.150 2.250 2.308 2.348 2.586 2.684 2.684 2.964 2.986 3.194 3.320 3.414 3.670 3.736 Write a program or give a general algorithm to...
  9. pratikpoddar

    Lots of quant problems: http://www.pratikpoddarcse.blogspot.com

    Lots of quant problems: http://www.pratikpoddarcse.blogspot.com
  10. pratikpoddar

    Russian Roulette (Difficult Version)

    I got this problem from Peter Winkler's Puzzle Book. I have not been able to solve it since 2 years now. In a room stand n armed and angry people. At each chime of a clock, everyone simultaneously spins around and shoots a random other person. The persons shot fall dead and the survivors spin...
  11. pratikpoddar

    Expected winning amount!!

    Nice problem. Both solutions (by @albertino and @peterruse) are interesting and correct. Thanks.
  12. pratikpoddar

    Lots of quant problems: http://www.pratikpoddarcse.blogspot.com

    Lots of quant problems: http://www.pratikpoddarcse.blogspot.com
  13. pratikpoddar

    Colored runs of cards

    Another solution posted on the blog link above: Number of ways in which we can have 52 runs is same as number of ways in which we can have 2 runs. Similar result holds for 52-k and k+2. This can be explained using the following construction : Suppose wlog we always start with red (this will...
  14. pratikpoddar

    Another variant of a classic

    Looks correct to me. Good one.
  15. pratikpoddar

    Colored runs of cards

    Answer: 27 Solution: http://pratikpoddarcse.blogspot.com/2011/05/coloured-run-of-cards.html
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