I think it's a safe assumption that the answer will be of the form:
The reasoning is that
Now, we want to get the longest sequence. To achieve this
For instance, if we try
Let's try another:
Going even lower is not an alternative, since:
Without a rigorous proof I'm going to say the combination is:
For the sake of this example, I assume a ball to be removed from the set once its position has been identified.
I got it in 10 steps. (Thanks for the improvements)
Please note that this solution may exit differently and take different logic in non-worst-case scenarios.
to move 3000 bananas by 1 km, camel consumes 5 bananas which with five trips. so not when number of bananas are less than or equal to 2000 the trips required is 3.
so to consume 1000 bananas
5x = 1000
move 3000 bananas for x=200 miles ( 5 trips). we are left with 2000 bananas.
now we have 2000 bananas and we can move bananas in 3 trips