4. Prince George has 100 coins, some of which may be counterfeit (possibly all or none). George can show the expert between 10 and 20 coins, and the expert will tell him how many of them are counterfeit. The problem is that the only expert in the area is Baron Münchhausen, and he exaggerates: the result given by the baron is always greater than the true number by some fixed (and unknown to George) natural number. The baron is not bothered by the fact that he might say "thirteen," for example, if he is given only twelve coins. Can George guarantee to find out which coins are counterfeit by consulting the expert fewer than 120 times?
Solution. It will work. We will submit $X$ random coins for examination, and then the same $X$ plus 1 more. If the baron says the same number both times, the added coin is genuine; otherwise, it is counterfeit.

Thus, we can divide the coins into groups of 10, and check each group for counterfeits in 11 queries: first, submit 10 other coins, and then add one coin from the group being checked each time. The total number of queries will be $11 \cdot 10 = 110 < 120$.

Criteria. The problem is worth 5 points.

Only the answer - 0 points.

Explained how to find the "error" - 1 point

The idea of adding a coin to the previous question - 2 points.

The correct algorithm is indicated, but it is not shown that the number of actions is less than 120 - 4 points.