Hi,

I'm new to the list, and dont have a definitive answer to the challenge,
but I do (maybe) have an idea that someone with more patience (and coding
skill!) can use to solve the problem:

In the Decimal system, there is a very easy technique for testing ANY number
for divisibility by 9. Its called "casting out nines" and can be best
illustrated with an example;

Take the number you want to test, lets say 12345, and add its digits
together;
1+2+3+4+5=15
then add the digits of the answer
1+5=6
Now because the answer is not 9 then the number 12345 is not divisible
by 9 (but, say, 123453 would be)

The basic proceedure of adding the digits is followed for ANY
length of test candidate, but you can take a short cut: any time you get
a 9 in the intermediate results you can discard it. Hence the name
"casting out nines". You continue adding until only one digit remains.

Now my idea: This method will work with any test number THAT IS ONE LESS
THAN THE RADIX. So to test for divisibility by 3, we could "cast out 3's"
if we were working to base 4. (or cast out 7's in octal or cast out
F's in hex)

That leaves the problem of converting the
number to be tested to base 4. A look at the binary equivalent of hex numbers
shows that a "tetrical" (or whatever you'd call base 4!) interpretation of
a number wouldn't be too hard to derive.

Sorry no code, like I said, I'm new...

--
Erik Grannells