Find a number with the following properties:
1. When expressed in decimal the number has each of the ten digits occuring exactly once.
2. When expressed in binary the number has the same number of 1s and 0s.

No leading zeros are allowed.

(In reply to hint based somewhat on computer findings by Charlie)

In fact, of the 2^31 = 2147483648 32-binary digit numbers without leading zero, C(31,14) =  265182525 have as many 1's as 0's. That's about 1 in  8.1.  Of course not all those are pandigital in base 10, but it gives and idea of the odds involved in finding one by chance.

Posted by Charlie on 2016-12-13 14:11:27