A number has four digits in hexadecimal.

arithmetic/digits/hex.multiples New

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Problem

A number has four digits in hexadecimal.  Written together, the number
and its double, triple and quadruple use each of the 16 hexadecimal
digits 0-9, A-F exactly once.  What is the number?  Variation: a
3-digit hexadecimal number, its double, triple and quadruple together
use each hexadecimal digit except 0 exactly once.  Why is each solution
unique?

Show solution

The answer to the 4-digit-n is:
   n = 258f
  2n = 4b1e
  3n = 70ad
  4n = 963c

and the answer to the 3-digit-n is:
   n =  da7
  2n = 1b4e
  3n = 28f5
  4n = 369c

You are correct that there is only 1 solution to both... but don't ask me why that is.
Before solving the problems, I simplified the domains of n to the
following (in hex):

4-digit-n:
  1023 <= n <= 3fed

3-digit-n:
  801 <= n <= fed

Can you see why?

-- Todd <sellertm@wmvx.lvs.dupont.com>

[ Editor: the posting gives no explanation of the uniqueness. ]