Question

Серёжа написал на доске в некотором порядке 2012 плюсов и 2013 минусов. Время от времени Леша подходит к доске, стирает любые два знака и пишет вместо них один, причем если он стер одинаковые.он пишет плюс, а если разные, то минус. Остался один знак. Какой?

Answer 1

Остался плюс. Так как он стерет больше минусов чем плюсов

Answer 2

Problem Analysis

Sergey wrote 2012 pluses and 2013 minuses on the board in a certain order. From time to time, Alex comes to the board, erases any two signs, and writes one sign in their place. If he erases two identical signs, he writes a plus sign, and if they are different, he writes a minus sign. Now there is only one sign left on the board, and we need to determine what that sign is.

Solution

To solve this problem, we need to analyze the number of pluses and minuses written by Sergey and Alex. Sergey initially wrote 2012 pluses and 2013 minuses. Alex then performed a series of operations, erasing two signs and writing one in their place.

Let's consider the possible scenarios:

1. If Alex erased two pluses, he would write a plus sign. 2. If Alex erased two minuses, he would write a plus sign. 3. If Alex erased one plus and one minus, he would write a minus sign.

Based on these scenarios, we can conclude that the remaining sign on the board will be a minus sign.

Conclusion

The remaining sign on the board is a minus sign.