Check if an array has duplicate numbers in O(n) time and O(1) space

We have array  a[ ]= {1, 2, 3, 4, 5, 6, 7, 8, 4, 10};
And we need to find a number which is duplicate in O(n) and Space complexity O(1)

Possible sizes of bus to carry n groups of friends

There are n groups of friends, and each group is numbered from 1 to n. The ith group contains ai people. 

They live near a bus stop, and only a single bus operates on this route. An empty bus arrives at the bus stop and all the groups want to travel by the bus.