MathDB

168

Part of 1972 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 168 All Soviet Union MO 1972 game with digits **** - **** =

Source:

7/3/2019
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 88 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 40004000, not depending on the second's behaviour.
2. The second can operate in such a way that the difference would be not greater than 40004000, not depending on the first's behaviour.
Digitsgame strategy