ISI 2021

Question

Let us consider the following 2-person game: the players alternately choose a number. The first player starts with a number between 1 and 10, and the players then pick up a number within the next ten of the number that his opponent has chosen earlier. The player who is able to select the number 100 first, wins the game. Can the first player pick up a number between 1 and 10 such that whatever may be the strategy of his opponent, the first player will be able to reach 100 first?

Answer 1

The first person to pick 100 wins => First person to pick 89 wins.

Player x picks 89 means player y is forced to pick from (90-99) , following which Player x can pick 100.

 

First person to pick 89 wins => First person to win 78 wins

First person to pick 78 wins => First person to win 67 wins

.

.

First person to pick 23 wins => First person to win 12 wins

First person to pick 12 wins => First person to pick 1 wins.

 

Since player 1, i.e. the first person to start picking can obviously pick 1, he can win the match.

 

.

.

.

Comments

if you pick 89 then i can pick any number from 90 to 100. So, you already lost.

---

Well, if someone picks 89, the next person has to pick within 10 of that which would be 90-99.