We are playing the Guess Game. The game is as follows:
I pick a number from 1 to n. You have to guess which number I picked.
Every time you guess wrong, I’ll tell you whether the number I picked is higher or lower.
However, when you guess a particular number x, and you guess wrong, you pay $x. You win the game when you guess the number I picked.
n = 10, I pick 8.
First round: You guess 5, I tell you that it’s higher. You pay 5. Second round: You guess 7, I tell you that it’s higher. You pay5.Secondround:Youguess7,Itellyouthatit
Third round: You guess 9, I tell you that it’s lower. You pay $9.
Game over. 8 is the number I picked.
You end up paying 5 +5+7 + 9 =9=21.
Given a particular n ≥ 1, find out how much money you need to have to guarantee a win.