Cryptotrump
Mr. Trump decides to post a random message on Facebook and he starts typing a random sequence of letters such that they are chosen independently and uniformly from the 26 possible english alphabets. Find out the expected time of the first appearance of the word COVFEFE.
The answer is 8031810176.
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1 solution
Say, in a casino, a person starts typing randomly. Now, a series of gamblers enter the casino one after the other. While the person in question types, the first gambler comes and bets Re 1 on the first word being C. If he wins then he bets again Rs 26 on the second letter being O, otherwise he loses all the money and quits the game.
“When the second letter is typed, another gambler comes in (who is unaware of the presence of the first gambler) and bets Re 1 on the second typed word being C. So again if this second gambler wins the bet he gets Rs 26. Each player continues betting until they lose and quit the game. This goes on and each gambler keeps on coming till the word COVFEFE appears. So if one thinks a bit then the sixth-to-last gambler will win and his total profit will be Rs 2 6 7 .