well...its simple as given in the article..
note that the numbers are all decimal numbers (not binary..in case
misled by just 0 and 1 in the number) therefore
if you have have k copies of 001 and k%3 == 0, then the sum of the
digits is divisible by 3 hence the number is divisible by 3 - The
Standard Test(The only digit is 1 and it occurs k times).

For the numbers such that k%3 <> 0, observe that the number mod k 9s
has the value of k1s. Since k9s is also divisible by k1s the original
number k*001* should also be divisible by k1s. This property holds
good for all k%3<>0.

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