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'Plate Spotting' printed from http://nrich.maths.org/

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I was in my car crawling along the M6 motorway a few weeks ago, thinking that it would be quicker to walk to the exhibition I was attending, when I noticed a line of four cars on the lane next to me with number plates starting with J, K, L and M and ending in the same letters, though each car did not necessarily start and end with the same letter.

The car with L as the last letter was not next to the car with L as its first letter but was next to the one with J as the first letter.

The two cars with M on their plates were at opposite ends of the group.
The car whose licence plate ended in K had the one starting in L in front.
The car with a plate starting with K was not next to the one starting with an L.

What were the start and end letters of each of the number plates and what order were they in?