Alternating numbers are numbers in which all digits alternate between even and odd. For example: 2703 and 7230 are alternating numbers, but 2730 isn't.
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 Math Olympiad, see this PDF