Bob has to find Alices hidden gold by questioning yes/no questions


I have this

Alice has n places to hide the gold v1,…,vn

Bob knows the probability of each place

Now Bob has to ask Alice YES/NO Questions to find the gold.

I have done it this way:

We order the placec by probability highest to lowest.

Now divide them by 2 so we have 2 sets

We ask whether it is in the high probability set or not

Now we divide by 2 again and ask if it is the highest one and so on

My prof told me that we have to get that he questions on average H(V) questions

But with this I am close with 2.576 to H(V)=2.47 but it’s not H(V) any better ways?

H(V) is the Entropy.