Question: A rat is placed at the beginning of a maze and must make it to the end. There are four paths at the start that he has an equal chance of taking: path A takes 5 minutes and leads to the end, path B takes 8 minutes and leads to the start, path C takes 3 minutes and leads to the end, and path D takes 2 minutes and leads to the start.
What is the expected amount of time it will take for the rat to finish the maze?
Answer: 9 minutes.
Each path has an equal chance of occurring and if B or D are chosen they will just add 8 or 2 minutes to the time because the rat must restart the maze: time = (1/4)*5 + (1/4)*(8 + time) + (1/4)*(3) + (1/4)*(2 + time). Time = 9 minutes.
Question: 8,549,176,320 What makes this number unique?
Answer: The said number has all the numbers from 0-9 exactly once and what is special is they are in lexicographical order of their English words. Where 8,549,176,320 becomes eight-five-four-nine-one-seven-six-three-two-zero. ... The number contains all the digits from 0 to 9.
Question: Hard, Harder, and Hardest are brothers. By age from youngest to oldest, it goes Hard, Harder, Hardest. Hard is half the age of Hardest who is 20 which means hard is 10. Harder has a two-year difference between the number of years older he is than Hard and the number of years younger he is than Hardest. Harder is closer to the age of Hard than Hardest. How old is Harder?