Arrange the digits from 0 to 9 into a number with inequality constraints

[jasen]

Arrange the digits from 0 to 9 into a 10 digit number (abcdefghij) which follow the rule :

• a < b > c < d > e < f > g < h > i < j
• difference between 2 adjacent digits is more than 4

Bonus puzzle :

Change the 2nd rule with :

• The digits follow the pattern : even,odd,even,odd....

[Logophobic]

 

4938271605

8967452301

Edited August 27, 2016 by Logophobic

[telesphorelalancette]

What do you think of 9-5-1-6-2-7-3-8-4-0.

[Logophobic]

I think 9 is not less than 5, and the difference between 5 and 1 is not more than 4.

The number I posted is the only solution and can be found logically. With the restriction that adjacent numbers have a difference of more than 4, the numbers 4 and 5 can only be adjacent to 9 and 0 respectively. The rest follows similarly.