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



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....
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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.

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