Teaser 2454: [French registrations]
From The Sunday Times, 4th October 2009 [link]
On holiday in France, I spotted two French cars parked side by side. The last two digits of their registration numbers represent the départements in which they are registered. Viewing the cars from the front and juxtaposing those two département numbers, I saw a four-figure prime number; and on going around the back and doing the same, I saw a different prime number.
Furthermore, the average of the two département numbers was prime, as was half their difference.
What were the two département numbers?
This puzzle was originally published with no title.
[teaser2454]
S2T2 
Jim Randell 8:34 am on 27 February 2026 Permalink |
Fortunately there is only one possible answer to the puzzle for 2-digit numbers, and it turns out they are valid département numbers.
The following run file executes in 84ms. (Internal runtime of the generated code is 4.6ms).
Solution: The two département numbers are: 39 and 43.
39 is Jura. 43 is Haute-Loire.
3943 and 4339 are primes, as is the mean of the two département numbers (41), and half the difference (2).
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