Alternating numbers are numbers in which all digits alternate between even and odd. For example:
7230 are alternating numbers, but
Numbers are very alternating when double the number is an alternating number as well, for example
3816 is very alternating, because
7632 is an alternating number as well.
The question to you is: how many 4 digits very alternating numbers are there? (the number can't start with one or multiple zeros)
Of course this problem can be solved by programming, but it can be solved mathematically as well! Good luck!
NB: I didn't come up with this puzzle myself, it's part of the Dutch "Wiskunde Olympiade": http://www.wiskundeolympiade.nl/files/opgaven/1e-ronde/2015/opgaven_en.pdf