33 days

33 days:

6->8 (8 eat 6 on 6th day and 8 live to 14th day)
2->3->9 (3 eat 2 on 2nd day, 9 eat 3 on 5th day and 9 live to 14th day)
8->9 (9 eat 8 on 14th day and 9 live to 23rd day)

1->5->7 (5 eat 1 on 1st day, 7 eat 5 on 6th day and 7 live to 13th day)
4->10 (10 eat 4 on 4th day and 10 live to 14th day)
7->10 (10 eath 7 on 13th day and 10 live to 23rd day)

10 eat 9 on 23rd day and it will live to 33rd day