My guess : 2^x / (1+x) >= 100, x + 1 = 12

This is the way I think.

Formulate all questions that ask for sets of specific numbers. For example, "Is the number 1,4,8 ... or 94?"
Let x be the minimum number of guesses required.
Construct a chart of 100 * x.

1 2 3 4 5 ... 100
1 Y N N Y N Y
2
.
.
.
x

Columns represent the possible value of the unknown number. Rows represent the question number.
The chart indicates the possible value of the unknown number asked in each question. Y means that the column number is asked as a possible value. N means that the column number is not. For example, if the first row only has V under 1, 4, and 100, the question is "Is the number 1, 4, or 100?"

If Alice is not allowed to lie, a number can be a possible value in case the answers to all questions match the chart. The value can be determined if only one number is a possible value.

Since Alice may lie, a number is possible if less or one answer to the questions does not match the chart. Therefore, x + 1 combinations of answers allow a number to be possible. Since there are 100 possible values, at least 100*(x+1) different combination is needed.

2^x >= 100*(x+1)
x >= 11

One last guess is needed to declare the unknown value.


I am not sure whether a combination of 11 questions can be formulated so that the answers under any two numbers have at least two differences.