95. Word game. Dr. Sylvester Sharadek announced that he can always guess the word you think of if he is allowed to ask 20 questions, to which the answers should be only "yes" or "no," and if the word is in the dictionary. Do you think he is boasting?
95. There are no dictionaries containing more than a million words. For example, if a dictionary has 500 pages, we will open it in the middle and find the last word on page 250, let's say, "narcissus." The first question should be: is the word we are guessing located after the word "narcissus" in the dictionary? If the answer is "yes," we will open the dictionary to page 375, and if "no," we will open it to page 125 and again ask about the position of the guessed word relative to the last word on the opened page, and so on. If at any point we get a fractional page number (for example, 62.5), we will round it up to the nearest whole number. After nine such questions, the search for the word will be narrowed down to one page. If there are 2 columns on this page, the 10th question will determine the column. In a column, there are no more than 64 words, and thus, the 16th question will lead us to one word, which, if we haven't already guessed the correct word, we will indicate to the person who thought of it.

The dictionary we used as an example contains no more than $128 \cdot 500 = 64000$ words. Since the number of words in a dictionary is limited to a million, it can contain no more than 16 times as many words as the dictionary considered above ($64000 \cdot 16 = 1024000$). For a dictionary with the maximum number of words, 4 additional questions will be required $\left(2^4 = 16\right)$, i.e., a total of 20 questions.

Thus, we see that Dr. Sharadek is telling the truth.