# You are a friend of Rohan. Do you suggest him to play first or second?

+1 vote
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Rohan and Karan are playing a game. There are digits from 1 to 9. The catch is that each one of them has to cut one digit and add it to his respective sum. The one who is able to obtain a sum of exact 15 will win the game?

posted Jun 9, 2014

## 2 Solutions

Rohan to play second

Explanation:
Let's suppose that Rohan plays first and he picks 9. Then Karan will definitely pick 8. Now, Rohan will have to pick 7 or Karan will pick 7 in his turn. But if Rohan picks up 7, then he will score 16 that is beyond 15 and will lose. So one thing is for sure, no one will be willing to start with the highest digits.

Suppose Rohan plays first and picks up 1, Karan will pick 2. Then Rohan will pick 3 and Karan will pick 4. Now Rohan will be forced to pick 9. The score is 6 to 13 and thus Rohan will have no chance of winning.

If Rohan Picks 9 after Karan has picked up 2, then Karan will pick 8 and the score will become 10 to 10. Thus Rohan will pick 3 as picking 7 will send him past 15. Now Karan will pick 4 and Rohan has nothing to pick for winning. Thus Karan wins.

Therefore, you should suggest Rohan to play second.

solution Jun 10, 2014

Rohan to play first
reason:
rohan will defenitely pick 9 first, then karan is forced to pick 6, otherwise in next chance rohan will pick 6 nd will win.
now, suppose rohan picked 9 in first nd karan picked 6 in first then in second round rohan will pick 1 bcz if he pick any no, whose add on will bring him near to 15 will make his chance less to win.
eg.
Rohan Karan
9+5 6+1................................then rohan never win but karan can 6+1+8
9+4 6+2................................then rohan never win but karan can 6+2+7
...likewise

solution May 6, 2016

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