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hk wrote: ↑Wed Feb 15, 2012 8:53 am
I fear that explaining in considerable more detail makes an otherwise nice problem almost unreadable.

But the nonsense about numberplates has already made an otherwise nice problem almost unintelligible. It would be better to ditch that entirely and write a problem statement which only gives the nice problem:

Seth draws with replacement random integers chosen uniformly from 0 to 999 until he has drawn two which sum to 1000. Find the expected number of integers drawn.