|Mar16-09, 03:24 AM||#1|
Seven digit base eight positive integer puzzle
N is a seven digit base-8 positive integer having the form ABCDEFG that uses each of the nonzero base-8 digits 1 to 7 exactly once, and satisfies these conditions:
(i) ABCDEFG is divisible by 7.
(ii) ABCDEF is divisible by 6.
(iii) ABCDE divisible by 5.
(iv) ABCD is divisible by 4.
(v) ABC is divisible by 3.
(vi) AB is divisible by 2.
Determine all possible value(s) that N can take.
|Mar16-09, 03:28 AM||#2|
I'm sure I could write a mathematica script to solve this, but does anyone have any good tricks to solve it by hand?
|Mar16-09, 10:28 AM||#3|
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