Playing with numbers: Balanced Pandigits

07072016, 04:40 PM
(This post was last modified: 07072016 04:43 PM by Joe Horn.)
Post: #1




Playing with numbers: Balanced Pandigits
I know this is not a Number Theory forum, but I see that many of you have played extensively with pandigital numbers (hereafter referred to as pandigits), so I'm hoping you can help me with a pandigit puzzler.
Let's call "balanced pandigits" the set of pandigits which are exactly 10n digits long AND which have each digit (0 through 9) occur exactly n times. The order of the digits doesn't matter; only the count of each must be the same. E.g. 77412551806806934392 is a balanced pandigit because it contains each digit (0 through 9) exactly twice. (As usual, leading zeros are not allowed). I hypothesized that balanced pandigits which were an exact power of an integer would be rare, so I set about looking for the smallest one. But a bruteforce search found NO balanced pandigits at all. I'm using UBASIC to raise x to powers as high as it could go before overflowing (very high!), with x starting at 2 and now it's above 30000. I'm mystified. (Maybe I'll try the HP Prime emulator and see if it's faster than UBASIC.) So my question is: Is it provable that no power of x (where x<1023456789 of course) can yield a balanced pandigit? If not, ARE there any? Thanks in advance! EDIT: OH GOOD GRIEF! Immediately after posting the above, the UBASIC program beeped and output 32043^2 = 1026753849. So... never mind! <blush> <0ΙΈ0> Joe 

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Messages In This Thread 
Playing with numbers: Balanced Pandigits  Joe Horn  07072016 04:40 PM
RE: Playing with numbers: Balanced Pandigits  Claudio L.  07092016, 10:54 AM
RE: Playing with numbers: Balanced Pandigits  Joe Horn  07172016, 06:37 AM
RE: Playing with numbers: Balanced Pandigits  Arno K  07152016, 08:23 AM

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