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  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
  16. pratikpoddar

    Another variant of a classic

    Another interesting solution at http://pratikpoddarcse.blogspot.com/2011/04/smallest-number-in-decreasing-sequence.html
  17. pratikpoddar

    Need for needles

    Right. Thanks. I was expecting that would mean that the integrals to the further right should be zero. But that is not the case. Thanks.
  18. pratikpoddar

    Need for needles

    I think it should be \(\int_0^{1-nh}\int_{x_1+h}^{1-nh}\cdots\int_{x_{n-1}+h}^{1-nh}1dx_ndx_{n-1}\cdots dx_1\) Right?
  19. pratikpoddar

    Handshakes

    Nice problem
  20. pratikpoddar

    platonic love

    agree with @peterruse Can you please elaborate on this calculation?
  21. pratikpoddar

    http://www.pratikpoddarcse.blogspot.com

    http://www.pratikpoddarcse.blogspot.com
  22. pratikpoddar

    Another variant of a classic

    Which method of differential equation are you referring to?
  23. pratikpoddar

    DE Shaw interview questions

    You are supposed to keep the cards side by side. Vertically is not allowed. The only information the other guy should have is the permutation. Nothing else. -- http://www.pratikpoddarcse.blogspot.com
  24. pratikpoddar

    DE Shaw interview questions

    This is very interesting. I saw this in Peter Winkler's book. Just sharing an interesting thought. At the first look, one feels that its not possible because permutation of 4 cards represent 24 different outcomes and the fifth card can be any of the 48 cards. So, this should not be possible. But...
  25. pratikpoddar

    Markov chain problem

    Thanks for the solution Bob
  26. pratikpoddar

    "Newspaper Beauty Contest"

    Nice post. Thanks
  27. pratikpoddar

    another die question

    I am intrigued. Can someone please find a flaw in koupparis solution?
  28. pratikpoddar

    another die question

    Koupparis, The probability of getting even has to be more. P(getting even | Game does not get over in first two chances) = P(getting odd | Game does not get over in first two chances) But game can get over in first two chances. And then the sum is even. Hence, prob of getting even > 0.5...
  29. pratikpoddar

    another die question

    For the expectation over time, the solution given by peteruse is correct. Let expected number of rolls be T. T = 5/6(1+T) + 1/6(1+1) So, T= 7 There are similar very interesting problems in coins space. http://pratikpoddarcse.blogspot.com/2009/10/lets-say-keep-tossing-fair-coin-until.html
  30. pratikpoddar

    A stockholder meeting

    Very interesting problem. You can get the solution at http://pratikpoddarcse.blogspot.com/2010/07/differing-views.html Cheers!
  31. pratikpoddar

    Seven-Eleven

    Well 79 is prime. So, one of the 4 numbers had to be 79, 158, 237, 316, 395, 474... So 711-(that number) would be: 632, 553, 474, 395, 316, 237... and 711000000/(that number) would be 90000, 45000, 30000, 22500. 18000, 15000... Since all the multiples have a lot of zeroes in them, I am more...
  32. pratikpoddar

    Seven-Eleven

    Information: a*b*c*d = 7.11 a+b+c+d = 7.11 a>b>c>d>0 100*a, 100*b, 100*c, 100*d are integers To find a. 711=3*3*79 (100a)*(100b)*(100c)*(100d) = 711000000 = 3*3*79*100*100*100 (100a)+(100b)+(100c)+(100d) = 711 Possible solution for (100a, 100b, 100c, 100d): (316, 150, 125, 120) So...
  33. pratikpoddar

    Interview Questions at JPMorgan Sales and Trading

    7 races 5 races for 25 horses. Eliminate last 2 in all the races. So, we are left with A1, A2, A3 B1, B2, B3 C1, C2, C3 D1, D2, D3 E1, E2, E3 Race between A1, B1, C1, D1, E1 and without loss of generality, say the result is A1>B1>C1>D1>E1 Then the candidates for top 3 are A1, A2, A3, B1, B2...
  34. pratikpoddar

    7.7 Jane Street interview questions

    Very interesting problem, I think! Classic example of Simpson's Paradox -- Pratik Poddar http://www.pratikpoddarcse.blogspot.com
  35. pratikpoddar

    Algorithms For Interviews

    Equal Probability of P and Q P(Q winning) = 1/64 + (6 choose 1)*1/128 + (7 choose 2)*1/256 + (8 choose 3)*1/512 = 1/64 + 6/128 + 21/256 + 56/512 = 130/512 = 0.253 Probability of P=7/12 P(Q winning) = (5/12)^6 + (6 choose 1)*(5/12)^6*(7/12)^1 + (7 choose 2)*(5/12)^6*(7/12)^2 + (8 choose...
  36. pratikpoddar

    Quantitative Interview questions and answers

    Generalized Semicircle Covering Points Problem A nice generalization of this problem can be found here If (n) points are drawn randomly on a circle, the probability of them being on the same semi-circle is (\frac{n}{2^{n-1}})
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