The data we get from the host is solely:

The variety of “sure” (or the variety of “no”, would not matter for the reason that variety of questions is fastened). This is as a result of we get again a set of unordered “sure” or “no”. So the one data we get is simply the variety of “sure”.

To have the ability to distinguish 100 numbers, we want no less than 100 totally different responses. Therefore:

We want no less than 99 questions (variety of “sure” may be 0-99, 100 potentialities).

Which may be simply achieved by asking a collection of questions within the type of:

“Is the quantity strictly bigger than N?” with N ranges from 1 to 99.

Then to guess the host’s quantity, we are able to merely reply with:

The variety of “sure”, plus 1. So 0 “sure” means the hidden quantity is 1. 31 “sure” means the hidden quantity is 32. And 99 “sure” means the hidden quantity is 100.