ASU 168 All Soviet Union MO 1972 game with digits **** - **** =
Source:
July 3, 2019
Digitsgame strategy
Problem Statement
A game for two.
One gives a digit and the second substitutes it instead of a star in the following difference:
Then the first gives the next digit, and so on times.
The first wants to obtain the greatest possible difference, the second -- the least. Prove that:1. The first can operate in such a way that the difference would be not less than , not depending on the second's behaviour. 2. The second can operate in such a way that the difference would be not greater than , not depending on the first's behaviour.