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 Not all a's are in (Posted on 2018-02-06)
A four-digit PIN number aabb, where a and b are distinct digits, is a multiple of 15.

Which values of a are not possible?

 See The Solution Submitted by Ady TZIDON No Rating

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I believe I have the solution.  Values that are not possible for a are {0,2,5,8}.  In order to be a multiple of 15 the only possible digits for b are {0,5} so the number ends in ..00 or ..55.  In addition the PIN needs to be a multiple of 3, so addition of all the digits a+a+b+b can not be a multiple of 3; also a has to be different from b.  So a can't be 0 or 5.  And checking the resulting possibilities we find that a cannot be {2,8} either since the sum of the digits for the following numbers are not multiples of 3:  {2200,2255,8800,8855}.
 Posted by Mark Hartman on 2018-02-07 17:44:17

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