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Sunday Times Teaser 2703 – Bastille Day

by Tom Wills-Sandford

Three French towns (A, B and C) issue their own car licence plates which respectively consist of the digits 1..9, 1..8 and 1..7 in some order. Only numbers divisible by 11 are used and all possible plates have been issued.

On Bastille Day these towns only allow in cars with their own plates and also require that the licence numbers are divisible by 5.

In the form ‘1 in …’ for each of A, B and C, what fraction of each town’s licensed cars will be allowed in?

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