Interview Question

Try this:

Five guys, all of different ages, enter a bar and take a seat at a round table. What is the probability that they are seated in ascending order of age?

Source: Susquehanna International Group

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  1. dollymix says:

    It doesn't specify that they need to be clockwise or counterclockwise ascending, so the chances are twice what jose has – 1/24.

    Put another way, the youngest guy can sit anywhere. Then the second youngest has to sit in one of the seats next to him (2/4 probability). Then the third and fourth youngest guys must sit in a specific seat each (1/3 and 1/2 probability, respectively) and the fifth guy sits in the remaining seat. (2/4)*(1/3)*(1/2)=1/12.

  2. Number people 1,2,3,4,5 meaning their ordinal age; there are five ways they can sit around a round table in increasing order of age: [ 1 2 3 4 5 ] [2 3 4 5 1] etc. There are 5 x 4 x 3 x 2 x 1 possible seating arrangements around the table, so dividing 5 by 5 x 4 x 3 x 2 we get prob = 1/24

  3. jack says:

    Does it have to be ascending in the clockwise direction, or in just any direction?

  4. NCB says:

    1 in 12 if it doesn't matter whether they are in ascending order clockwise or counterclockwise. If we require a specific orientation, such as ascending order clockwise, then 1 in 24. (NCB)

  5. @cliffelam says:

    The great thing about questions like that is that they identify companies where I wouldn't want to work…

    Men tend to try to sit next to the most powerful person at the table, who is also (generally) the oldest, so most powerful at point.x, second and third at x-1,x+1, etc. With an allowance for a favored student.


  6. Good point. Felled by my unspoken assumption of what increasing means.

  7. Esteban says:

    Somewhat vaguely specified. If by 'ascending' order, one means they are ordered youngest to oldest, with no distinction between clockwise and counterclockwise, the probability is 2/(4!) = 2/24 = .083.

    Start with the oldest guy. There are 4! = 24 orderings of the other four guys. One of which will correspond to ascending order in the clockwise direction, the other in the counterclockwise direction.

    If 'ascending' means one direction, e.g., clockwise, then it's 1/24 = .042.

  8. Dean says:

    Around the same probability that asking this question will help you find the right person for the position. Saying that I think the odds are better than 1 in 12 as it is not a random sample.

  9. PatS says:

    I also get 1/12, but I don't assume a fixed number of seats at the table :-)

    3 guys can sit down and they are always in increasing order, either clockwise or anticlockwise. the 4th must sit between #1 and #3 – 1/3 chance. the last must sit between #4 and #1 – 1/4 chance. result = 1 * (1/3) * (1/4) = 1/12.

  10. duhduh says:

    0 chance, either ascending or descending orders require an edge which the round table does not provide

  11. Mufa says:


  12. idea2go says:

    What most people are missing is that the interviewer was an HR person that is really trying to get at your attitudes on job etiquette.  That totally skews the results. 

    (I got 1/12 also, but only 1.7% once they lined up at the urinal)

  13. Wes says:

    Assuming that any one of the men has a 50% chance of being younger than another.

    First gentleman has a (1/2)^4 chance of being the youngest

    Second gentleman has a (1/2)^3 chance of being younger than everyone everyone after him

    The total probability of each being the youngest of those after them would then be (1/2)^10

  14. Trick question says:

    I'm with duhduh. It's a trick question. They're seated in a circle, and even assuming they're ordered (1,2,3,4,5), since it's a circle you go 1->2->-3->4->5->1->2… etc. etc.

    That might strike you as a trick answer, but the tip-off it's a trick question is the "round table" specification. What relevance is that otherwise?

    Questions like these are entertaining, but if anyone ever asks you something like this in an interview, go somewhere else. It just shows the firm has so little confidence in its ability to spot talent it reduces the effort to childish games like this.

  15. tyaresun says:

    A big fat zero probability. It is impossible to have an ascending order on a ROUND table.

  16. stan.k says:

    The question assumes the table only has five seats. Does it?

  17. Karthik says:

    Clockwise or anti-clockwise? ;-)

  18. mark says:

    to the people who think you should go somewhere else when your asked a question like that. you should research the firm and you'll know exactly why the question was asked, idiots

  19. xalmeda says:

    The probability should be zero right ? because they are sitting in a round table