Enigma 1710: Carregio
8 August 2012
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From New Scientist #2877, 11th August 2012 [link]
Since the second world war, car registrations in my country have consisted of three parts: the first is the four-figure year of manufacture, the second is made up of two letters, and the third consists of a number which, in my case, has three digits. However, we are now switching to all-digit car registrations, consisting of three parts. Existing registrations such as mine will be adapted by changing the two letters to a number by replacing A by 1, B by 2, and so on, so that, for example, GL would become 712.
The three numbers making up the three parts of my car’s registration will then all be multiples of 18, but none will be a perfect square. And overall the registration will use each of the digits 0 to 9 exactly once.
What is my car’s registration before the changes?