Hey Stool....
Just read everyones comments and tips but nobody picked up on the 5 o'clock position of the hole....now remember that so far no one has seen this hole apart from you and Border engines.
If you are looking at the side of the engine then the 5 o'clock position equates as very close to the inlet valve, this then leads me to believe that you have some sort of air leak on that cyclinder. This will produce the lean mixture that could cause the piston crown to overheat and literally get blown in by the compression pressure (bit like welding aluminium with an oxy/acetylene torch...one second its there then plop its gone).
Potentially the fault could be air leaking in around the injector, or the vacuum blanking rubber plug (underside of the throttle body) is missing/ pulled off by some arse hole/holed or too loose.
Please check very carefully that there are no air leak problems, I doubt that the injector was the cause, it is not unusual to find that there is difference between the two. Those fitted to multi-cylinder engines can sometimes be well out delivering different quantities of fuel over the same period of time.
If the hole was caused by detonation you would have noticed a rattling type of sound when the engine was pulling hard and normally this causes the rider to cack themselves and pull over to find out what the noise is.
Continual running with a Remus or any other free flowing exhaust will usually only affect the exhaust valves after some condiderable time at high engine revs over quiter a distance (eg 4-5,000 miles) if no mixture adjustments have been carried out.
What are the spark plugs like and are they the correct grade?
If the hole is a 'mechanical' rather than melted hole then you have to assume something has fallen into the inlet track and got past the inlet valve, this will be evident by serious marks to other areas of the piston crown and cylinder head combustion chamber.
The damage to the cylinder was most likely ther top piston ring siezing due to no boundary lubrication and due to overheating and subsequent expansion and no where to go the ring has grabbed the cylinder wall.
Sorry about your engine, this is not normal BMW engine trouble and the comments about the car engines does not relate to your type of engine. Check elsewhere on the site and you will see that people remove the catalytic convertor so as not to harm it when travelling abroad using dubious fuel quality.
Pity there was no picture it could tell people an awful lot.
Hope you cure the problem relatively cheaply
