1) Find all the 0 to 9 pandigital numbers (without leading zero) that
have the largest power of 3 as a factor.
2) One of these numbers has a very interesting property. What is it?
*an x to y pandigital number is an integer that contains all the digits from x to y and only those digits once each, for example 1234 is 1 to 4 pandigital but not 1 to 9 pandigital*
I do not understand the specifications. I assume that a "0 to 9 pandigital" without redundancy, and not starting with zero, means an integer between 1023456789 and 9876543210 which uses each digit once. The additional spec is that it "have the largest power of 3 as a factor". This is ambiguous, but presumably means we are to test divisibility by the highest power of three which exactly divides a pandigital.
The largest power of 3 which could be a factor of a ten digit number would by 20. There are no multiples of 3 from powers 20 down to 16 which divide a pandigital (with integer result).
There is exactly one which divides by 3 ** 15, viz.
14348907 * 505 = 7246198035
I have no idea what the proposer might consider a "very interesting property," but do not reach this since (1) suggests an interpretation is needed which finds "all" (presumably more than one) candidate pandigitals.
I'll see what others have answered, or await clarification of the problem.
Uncertain
