Determine the largest integer A such that for K=1,2,3,...,length(A) the first K digits of A form an integer divisible by K.
For example, for 56165, 5 is divisible by 1, 56 is divisible by 2, 561 is divisible by 3, 5616 is divisible by 4 and 56165 is divisible by 5.
You are hot on the trail of an enemy, who is hiding in one of 17 caves.
The caves form a linear array, and every night your enemy moves from the cave he is in to one of the caves on either side of it.
You can search two caves each day, with no restrictions on your choice. For example, if you search (1, 2), (2, 3), ..., (16, 17), then you are certain to catch him, though it might take you 16 days.
What is the shortest time in which you can be guaranteed of catching your enemy?
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Bonus: 
