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On a train, Smith, Robinson, and Jones are the fireman, the brakeman,
and the engineer (not necessarily respectively). Also aboard the train
are three passengers with the same names, Mr. Smith, Mr. Robinson, and
Mr. Jones.
(1) Mr. Robinson is a passenger. He lives in Detroit.
(2) The brakeman lives exactly halfway between Chicago and Detroit.
(3) Mr. Jones is a passenger. He earns exactly $20,000 per year.
(4) The brakeman’s nearest neighbor, one of the passengers, earns exactly three times as much as the brakeman.
(5) Smith is not a passenger. He beats the fireman in billiards.
(6) The passenger whose name is the same as the brakeman’s lives in Chicago.
Who is the engineer?
Want to know who? Click Here!
Would you like to read question first?
Let's list all the clues once again here.
(1) Mr. Robinson is a passenger. He lives in Detroit.
(2) The brakeman lives exactly halfway between Chicago and Detroit.
(3) Mr. Jones is a passenger. He earns exactly $20,000 per year.
(4) The brakeman’s nearest neighbor, one of the passengers, earns exactly three times as much as the brakeman.
(5) Smith is not a passenger. He beats the fireman in billiards.
(6) The passenger whose name is the same as the brakeman’s lives in Chicago.
Since as per (2), the brakeman lives exactly halfway between Chicago and Detroit, locations Chicago or Detroit can't be nearest to him. Hence, the passenger that (4) is suggesting must be nearer to brakeman than Chicago and Detroit.
Now as per (1), Mr. Robinson lives in Detroit, means he is not the nearest to brakeman. Mr.Jones earning is $20,000/year as per (3), which is not evenly divisible by 3. Hence, the passenger (4) is pointing is not Mr.Jones.
So neither Mr. Robinson not Mr.Jones but Mr.Smith is the nearest neighbor.
Now Mr. Robinson lives in Detroit and Mr.Smith is living in between Chicago and Detroit but nearer to brakeman. Hence, Mr. Jones must be living in Chicago.
According to (6), Jones must be name of the brakeman as he is sharing his name with the man living in Chicago.
And if Smith is not fireman as per (5), he must be an engineer!
A sultan has 14 daughters. He decides to tell every night four of his daughters a fairy tale, but in such a way that every night, there will be
another combination of four daughters. How many nights will keep the
sultan busy telling fairy tales?
Find number of nights here!
Story behind the title?
For a moment, let's name all the daughters as A, B, C, D, E.....N.
There are 14 x 13 x 12 x 11 = 24024 combinations of daughters. But in these combinations, lots of combinations are repeated. For example, ABCD combination is same as ABDC or DABC etc. There can be 4 x 3 x 2 x 1 = 24 combinations while considering group of 4 daughters here for example it is A, B, C, D. For these 24 combination we should count only 1 as a unique combination.
Hence for 24024 combinations, we have 24024/24 = 1001 unique combination.
In short, Sultan would be busy for 1001 nights in telling fairy tales to his 14 daughters in unique combinations.
