Number Plate Puzzle

Except for some special vehicles (like military vehicles), all other vehicles have license plates with four digits (lower digit numbers can be assumed to be four digit numbers with preceding zeros). Assume that these numbers are uniformly distributed among the vehicles of a city and also assume that vehicles with number plate 0000 also exist.

Now for every number plate \(abcd\), we consider the difference \(S = \lvert ab - cd\rvert\) and average this answer over a large number of vehicles. What is the integer part of the average that is obtained?

Note: For example, for a number plate \(1234\), we have \(S = |12-34|=|-22|=22\)).

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