Fun & Game Puzzle

Puzzle: You are playing a game with your friend Jack. There are digits from 1 to 9. You both will take turn erasing one digit and adding it to your score. The first one to score 15 points will win the game. Would you want to play first or second?

PS: The sum should be exactly 15.

This is classic Fun & Game Puzzle.

interview riddle
Solution:
Suppose you are player 1 and your friend is player 2.

You will start by picking 1. If your friend picks up 2, then you will pick 3 and your friend will pick 4. Now this will force you to pick 9. The score now becomes 6 to 13 and you have no chance of winning. Thus you pick up 9 after your friend picks up 2. Then the player 2 will pick 8. The score will now be 10 to 10. Thus you pick the number 3 as picking 7 will throw him over 15. Your friend will pick 4. Now you will have no move, thus your friend will win.

Thus, You pick up 9, then your friend will choose 8. Now you won’t be able to pick up 7 as then your sum will be more than 15 which will make you lose. But then your friend will pick 8 and will win.

So it will be wise to play second.

4 Thoughts on “Fun & Game Puzzle

  1. play second

  2. Soumya Chaurasia on September 4, 2014 at 10:17 am said:

    ?????????????????

  3. anuj saini on February 1, 2015 at 6:24 pm said:

    solution is completely wrong
    there would be these sets
    (9,6),(9,5,1),(9,4,2),
    (8,7),(8,6,1),(8,5,2),(8,4,3)
    (7,6,2),(7,5,3)
    (6,5,4)
    (5,4,3,2,1)
    we have choose numbers from these combination to make 15

  4. Shailendra Pandey on February 13, 2015 at 1:36 pm said:

    you–96
    your friend–87

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