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You can make 27 unique three-digit numbers using the three digits 0, 1, and 2.

i.e. for each of the three digits abc, there are 9 possible orders of those, from aaa to ccc.

The 9 starting with 0:

000

001

002

010

011

012

020

021

022

* the combinations are the same as the numbers 0 to 26 expressed in base 3 (000 to 222)

26 base 3 = 222 = 18 + 6 + 2 = 26

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