Train carriages in the Czech Republic

No, there is no such algorithm. Your only option is to check the train carriage map in advance on the web or the train station. The carriage numbers are not meant to be indicative for the end users and therefore don't follow a fixed pattern.

Source: personal experience riding trains in Czech Republic. Unfortunately nowhere does Czech Railways state an explanation for the carriage numbering, so it's hard to prove a negative.

There is apparently no good system which you can use without external source of information. However, there are a few tips you can use to determine the position of your carriage with a good chance of success.

1. Look around the station and platform. There is usually a board which contains diagrams of nearly all the longer trains which go through the station. Ask the station personnel where it is if you cannot find it. Ususally it's in the station lobby or somewhere on the platform.

2. Look at servers like http://www.vagonweb.cz/razeni/ or http://www.zelpage.cz/razeni/ . These are something like Seat Guru for airlines - they contain detailed information about the individual carriages, their age and state of (dis)repair, so you can pick the best place to sit. Also, seat reservations are free in the vast majority of trains as long as you buy the ticket online at least an hour or so before departure.

3. While the carriage numbers are not perfectly ordered, they are always ordered to some degree. So if the train is coming into the stations and you see the carriage numbers on the doors, you get a pretty good idea where to go. The chaos in carriage numbering also does not apply to most modern trains, so you can be fairly sure that they will be well-ordered if you go by a RailJet or InterPanter.

I think the best way to deal with the number is to read it as arbitrary identifier number. maybe it is the identifier within the carriage depot. If you are curious, ask a station personell.

When entering the train, check the carriage destination to be same as Yours, check the class and find your compartment. This is displayed on the carriage display (new/upgraded coaches) or in the door window, there is Train ID and highlighted stations. If you take a wrong compartment, you will be asked to change it, if necessary.

You can also look for conductor and ask them when boarding. They should be near the carriages where their assistance is expected (cargo, bike, disabled) or near the last carriage.

What nobodody has written so far: In most european countries the platforms are divided in sectors (mostly A-E, sometimes even up to G) and there are either posters or electronic boards that indicate what carriage number you can expect to be provided near which sector. On the platform the sectors are usually written right next to the platform number (1A, ...).

When you arrive at the station go to the specified platform as in many cases the posters that show the order of the coaches are only located directly on the platform. Locate the section of your carriage and walk to the section that is stated on the board. The coach with your number should stop somewhere near.

AFAIK the longest passenger train you can expect to come upon won't be more than 400m (~1300 feet) in length, so for most people it should be possible to locate the the carriage while the train stands at the platform.

I don't know if this is applicable for the Czech Republic, too, but at least here in Austria the voice announcements also give information (even in english) on the train layout: "The first class is located in section A. The carriage with space for wheelchars is located in section C". The boards also often display if the coaches are not positioned according to plan.

And what others have written so far still applies - you can always pass between coaches, so if you get on the wrong one it's no problem and also ask the train/station staff.

Is there any system or algorithm how to find out what carriages a train consists of? Do these numbers have any meaning? Can I expect the carriage 369 will be right behind the locomotive, or at the end of the platform?

No, there is no algorithm, not for the passengers at least. The numbers must be unique in one train, that's all. They are attached to the carriages as the train is assembled, they're not permanent.

This information would be very useful, because the platform is often crowded and I don't want to run over the whole platform looking for my carriage.

You can sometimes find a "map of train" just like the one you attached. Which is still "more what you call guidelines, than actual rules", because problems can happen that require changing of cars and railroad would rather have the train misordered or backwards than 20 minutes late.

Bottom line is: every train is unique. You need to either walk it entirely or get a map. Car numbers are displayed on the cars so you can read them as train arrives on the platform. You can either spot your car before it stops or at least you can tell "mine must be in the other half". In any way, if you think you're running out of time, just board the closest car and then you can continue looking from the inside.

/edit: I forgot one very important thing: often sleeper cars cannot be walked through, that is the doors to next carriage are locked. It's so when there is a dedicated attendant for every sleeper car. He checks tickets before letting passengers in, so there is plenty of time to find your car.

If you want to understand the logic behind it:

The train-car-seat system is much like city-street-house address. There can be a Main Street in more than one city, or there can be a city where there is none. Sometimes Main Street leads to the City Square but sometimes it's located in entirely different part of the city. Similarly house numbers sometimes are even on there right, odd on the left, sometimes counting towards city center or sometimes away from. And of course then you get occasional empty plot which causes a hole in numbering.

BTW, the example you've included is super-complicated, because this looks like multiple destinations train, which gets split or merged on the way and different parts go (or come from) different destinations. Eg imagine if they take a train from Prague and then join it mid-way with a train from Bratislava, have the result drive most of the way and then split it into 2 another trains, one to Krakow and one to Kiev. Now you basically have 5 different combinations, and you have to ensure that all cars bear unique numbers, and that specific cars from each of starting points arrive to each of destinations. There is no way you can achieve consistent and monotonic numbering at all times. And there is no need, as even the least oriented passengers will literally have hours to find their cars.

the reason is actually pretty logical, even though it doesn't appear so at first glance: Carriages numbers are assigned by UIC (International Railway Union). Every train operator has unique interval. The Czech Railways has something like 35x - 37x, unfortunately I don't recall that interval exactly. As every coach has unique number, it is possible to identify coaches in train even when it's composited from coaches of multiple railway operators/ direct coaches as in OPs case - if they were numbered 1 - x, there could be several coaches of same number. It should be described in detail in some UIC document...

Source: The Czech Railways FB page, however, it is some time since then and it is buried somewhere on their timeline.

This numbering is beneficial when trains exchange carriages. Nowadays the daytime trains here in Czech republic do not exchange carriages, some of them leave some carriages in a station on the way to save money when having less passengers going to the final station.

But the nighttime trains stop in some big stations and exchange carriages so people do not have to wake up and change trains in night. In that occassion such large numbers can provide uniqueness, so they know that let's say carriage 369 goes from Budapest to Berlin but 370 goes from Budapest to Warsaw, so the railway workers that exchange carriages between two trains in B?eclav know exactly which ones to exchange.