# Why do I always catch Bus B instead of Bus A?

Each day, I will catch either Bus A or Bus B on my journey home from work. Both take the same route, run every ten minutes, and take the same time to reach my destination. Neither is busier, cheaper or less comfortable, and I have no preference for one over the other.

I finish work at different times every day, somewhere between 4-6pm. I hustle to the bus stop and jump on whichever bus is there.

And yet 90% of the time, I take Bus B. Why?

• If you got the riddle from somewhere else, you're supposed to give attribution. – Acccumulation Dec 18 '18 at 21:59
• I drive Bus B and know it is SO much better than Bus A. – Keeta - reinstate Monica Dec 19 '18 at 13:13
• Can confirm Keeta's assertion. I'm Bus B. – corsiKa Dec 20 '18 at 3:25
• The title says you always catch bus B, but your description says you catch bus B 90% of the time (which is not the same as always). – Fodder Dec 20 '18 at 22:18
• Surely this puzzle is such an old classic that it has been asked here before? At least, that's what I thought - I've searched, but haven't been able to find anything. – Jaap Scherphuis Dec 21 '18 at 14:37

It's probably due to scheduling.

If Bus A runs on the 0s, and bus B runs on the 9s, then, given a random arrival time at the stop, you have a 1 minute window to catch A, and a 9 minute window to catch B

• What does 0s and 9s mean? I don't understand this answer – Telokis Dec 19 '18 at 9:41
• @Telokis it means that, for example, bus A arrives at 12:00, 12:10, and so on, while bus B arrives at 12:09, 12:19, and so on. If you arrive to the stop at a random point of time and take the first bus that arrives, then bus B will be taken 90% of the time. – votbear Dec 19 '18 at 9:46
• "Neither is busier" ? In this case BusA should be significantly (9 times busier) if you take into consideration that people arrive at the station uniformly – Shai Aharoni Dec 19 '18 at 11:40
• @ShaiAharoni: If the two lines come from different places before they reach the OP's stop, the lopsided scheduling would not yet have caused A to be busier at the point that matters (namely where the OP boards the bus and finds out if he gets a seat or not). – hmakholm left over Monica Dec 19 '18 at 14:22
• @shaiaharoni I took that to mean neither was crowded. A bus with 10 people on it isn't crowded enough to make me wait for a bus with 5 people on it. i.e. I can find a seat, and maybe even have an empty seat beside me. – Chris Cudmore Dec 19 '18 at 15:58

Bus B has its terminus at your stop so it tends to be sitting there waiting for its scheduled departure

• +1, I think this is pretty much it. The important thing not accounted for is how long the buses remain at the stop, and clearly bus B remains longer at this particular stop. We know they both arrive every 10 minutes, but bus A likely remains at another stop (or both additional stops) for longer. The problem with the 'on the 9's' answer above is that it assumes that one bus will leave when the other arrives, but doesn't account for both buses remaining there waiting for passengers at the same time (which would not result in a 90% use of bus B) – RhinoWalrus Dec 21 '18 at 15:25

Is it because

Bus B is a weekday bus and Bus A only runs starting on weekends. If Bus A starts running Friday afternoons, that would mean that Bus A would be caught 10% of the time (Friday evenings) while Bus B is caught the remaining 90% (M-F mornings, M-Th evenings).

The one thing that's not been mentioned so far:

Everything else in the question discounts there being a difference in the bus or the routes, therefore the difference must be in where you work. Should the two busses have the same route but be different then they are most likely running opposite directions to each other, and you tend to take the stop that is slightly closer to your work: on the same side of the street - but sometimes you'll cross the road and take the bus heading the other direction, either due to traffic (the crossing), or actually seeing it turn up just as you get to the empty stop on this side.

Maybe although you "finish work at different times every day, somewhere between 4-6pm",

90% of the time you finish at 4:05, when bus B arrives, and the other 10% of the time you finish at 4:11, when bus A arrives. You didn't preclude an extremely narrow distribution of departure times like this. (Of course, it works equally well for distribution between any two other times in that range.) Unless "different times every day" is meant to literally mean that no leaving time is ever repeated, in which case this solution could be modified to leaving at 4:05:00, 4:05:01, 4:05:02*, ... 90% of the time,

etc.

*Choose a smaller increment to fit, depending on the length of your career.

I think it's a matter of distance

My guess is that both busses arrive and leave at the same time. It just happens to be that Bus B is closer to your workplace so it's the first one you hop in. In case bus B is fully occupied, you walk over to the next bus.

• They both take the same route though... – Albert Rothman Dec 20 '18 at 21:17
• Still, Bus B could be closer because it's behind/in front of the other bus, whichever position is closer to the workplace. It saves at least 1 bus length of walking ;). – Stefan Jan 9 '19 at 11:33

Based on distribution:

Either they are more Bus B than Bus A (9 Bus B but only a single Bus A for example), like a Bus B every 10mn dispatched 1mn apart each, the 9th being a Bus A. The Bus B is likely the general route, and one out of ten bus make a different route after your home and, as such, are labelled A

Based on logic:

If there are 50% probability to get any bus, then you are the driver of Bus A. Thus to go home, you need to walk down your own bus, let the new driver jump in, and wait for the next bus (Bus B). The 10% of the time you take a Bus A is when you have to drive another bus (one day per your 5 days work week, thus 20% of your the times), and then you have 50% of chances to have a Bus A or Bus B.

My first guess would be

There's no reason, it's just a matter of coincidence. Though if the odds were perfectly distributed you'd ride 50% of the times on each, there's always a chance that you'll ride one more often than the other, whether it's 5% or 50% more times.

It must be

You have no preference on one buss over another but your annoying neighbor that also go to the same way prefers bus A and so you take bus B to avoid him.

There is another employee in another office who get Bus A 90% Of times. Tho keep balance. This is law of nature.

May be Bus A and B is there from home to work.
But from work to home only Bus B is there

• The question only speaks about travelling home, so I'm afraid your answer does not provide a solution. – hat Dec 19 '18 at 8:29
• @jtest Hello and welcome to PSE. Please hide your answers in spoilers using the >! prefix. – rhsquared Dec 19 '18 at 8:47