When three professors are seated in a restaurant, the hostess asks them: “Does everyone want coffee?" The first professor says: “I do not know." The second professor then says: “I do not know." Finally, the third professor says: “No, not everyone wants coffee." The hostess comes back and gives coffee to the professors who want it. How did she figure out who wanted coffee (10)

When three professors are seated in a restaurant, the hostess asks them: “Does everyone want coffee?" The first professor says: “I do not know." The second professor then says: “I do not know." Finally, the third professor says: “No, not everyone wants coffee." The hostess comes back and gives coffee to the professors who want it. How did she figure out who wanted coffee (10)

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter19: Probabilistic Dynamic Programming

Section19.4: Further Examples Of Probabilistic Dynamic Programming Formulations

Problem 7P

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Tom and Jerry recently saw the movie inception. Inspired by that movie they decided to play a complicated game. Analogous to the movie inception, Jerry is the dreamer and Tom is the thief who enters Jerry's dream in order to extract the secret code. Tom wins the game if he is able to extract the secret code, else Jerry wins the game. Note that here Tom has to extract the idea from Jerry. Tom after performing a lot of mathematical analysis finally ended up to one last step for which he requires a little computation. He has got an array of positive integers. If atleast one of them is prime, he will be able to crack the secret code and win the game, else Jerry wins the game. Input The first line contains a single integer t (1≤t≤106) the number of test cases. Description of each test case is as follows. The first line of each test case contains a single integer n (1≤n≤2⋅106) the number of elements in the array. The second line of each test case contains n positive integers…
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