Sergei and Lena have several chocolate bars, each weighing no more than 100 grams. No matter how they divide these chocolate bars, the total weight of the chocolate bars for one of them will not exceed 100 grams. What is the greatest possible total weight of all the chocolate bars?
It is possible to divide the chocolates "almost equally" - such that the difference in weight between the chocolates given to Lena and Sergei does not exceed 100 grams.

## Solution

First, give all the chocolates to Sergei and then start giving one chocolate at a time to Lena. Initially, the weight of the chocolates with Sergei is greater, but there will come a moment when the weight of the chocolates with Lena is not less than that with Sergei. Let's say at this moment the chocolates with Sergei weigh $A$ g (by condition $A \leq 100$), the chocolates with Lena weigh $B$ g, and the last chocolate we moved weighed $C$ g. Before moving this chocolate, the total weight of $B-C$ chocolates with Lena was not more than 100 g. Thus, the total weight of all the chocolates $A+(B-C)+C \leq 3 \cdot 100=300$ g. Example: three chocolates, each weighing 100 g.

## Answer

300 grams.