You are in a room with 2N Plaminians and C locked chests. One of the chests contains a treasure. Half of the Plaminians are consecrated, and know which chest contains the treasure. The other Plaminians do not know which chest has the treasure. All of the Plaminians know which ones are consecrated. You do not know which Plaminians are consecrated, or which chest has the treasure.
The Plaminians have agreed that you may ask each one a yes/no question, and they will answer truthfully if they know the answer, and randomly if they do not know.
What sequence of questions will give you the greatest chance of locating the chest with the treasure? For what values of N and C is success guaranteed?
If C is 1, then of course success is guaranteed.
Suppose N is two or more. We'll start with N=2, so there are 4 Plaminians, a, b, c and d.
Ask a if b is a Plaminian. Each time you get an affirmative answer, ask the confirmed Plaminian whether the next chest in the sequence 1, 2, ... has the treasure. At any time you get that go-ahead to ask about the treasure, you won't be able to ask about the subsequent Plaminian and so must start over again, if you get a negative answer about the treasure. So you'll build up a list of unknown status Plaminians. That's unfortunate, as if the number of confirmed non-consecrated Plaminians reaches N, you'd know the rest are all confirmed.
Details to be worked out...
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Posted by Charlie
on 2024-03-20 07:35:38 |
a start for a way to go
