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8

I took the practical approach and came up with a strategy that could be optimal (I have not tried to prove it). In the worst case scenario it takes: I made a drawing to show my strategy. The yellow squares are the rooms the police officer looks into that night, the black squares are rooms in which the thief logically cannot be.


7

This is a very nice 2-dimensional variation of this question.


0

I don't know how to do the exact maths (maybe someone else can help me out) but:


14

I managed to find the 8 in So we are trying to find the 5th largest card in a bunch of 12, by measuring them in batches of four. Here's my strategy: Now we have identified, for certain, a couple of cards we can exclude: A1 and A2 (both have at least 8 cards smaller than them), and B4, C2, C3 and C4 (all have at least 5 cards bigger than them). We also have ...


5

I can do it in Note: Continuing... Assume the worst case. Any other results would obviously be easier to solve. For any of these options: Thus, we have completed the process and identified card 8 in at most Note, that as a side-effect of identifying card 8, we also identified cards 12, 11, 10, & 9. There might be a more efficient option to ...


5

I can do it in:


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