Can Kolya Win at the Stone Pile Game?

  • MHB
  • Thread starter zen1
  • Start date
  • Tags
    Game
In summary, Kolya and Vitya are playing a game where they take turns dividing piles of stones into smaller piles until there is only one stone in each pile. The player who leaves all piles with only one stone wins. It is not possible for Kolya to win every time, but it is not clear who will win in certain situations.
  • #1
zen1
1
0
KOLYA AND VITYA PLAY THE FOLLOWING GAME. THERE IS A PILE OF 31 STONES ON THE TABLE. THE BOYS TAKE TURNS MAKING MOVES AND KOLYA BEGINS. IN ONE TURN A PLAYER DIVIDES EVERY PILE WHICH HAS MORE THAN ONE STONE INTO TWO LESSER ONES. THE PLAYER WHO AFTER HIS TURN LEAVES ALL PILES WITH ONLY ONE STONE IN EACH WINS. CAN KOLYA WIN NO MATTER HOW VITYA PLAYS?

I'm pretty sure that Kolya can't win every time but I'm a bit confused on the actual math behind it, would love some explanations. Thanks!
 
Mathematics news on Phys.org
  • #2
zen said:
KOLYA AND VITYA PLAY THE FOLLOWING GAME. THERE IS A PILE OF 31 STONES ON THE TABLE. THE BOYS TAKE TURNS MAKING MOVES AND KOLYA BEGINS. IN ONE TURN A PLAYER DIVIDES EVERY PILE WHICH HAS MORE THAN ONE STONE INTO TWO LESSER ONES. THE PLAYER WHO AFTER HIS TURN LEAVES ALL PILES WITH ONLY ONE STONE IN EACH WINS. CAN KOLYA WIN NO MATTER HOW VITYA PLAYS?

I'm pretty sure that Kolya can't win every time but I'm a bit confused on the actual math behind it, would love some explanations. Thanks!

Hi zen! Welcome to MHB! (Smile)

Let's work back from the end.
Suppose there is only 1 stone, who will win?
What with 2 stones? And 3?

Now it becomes more interesting.
Suppose we have 4 stones, to win, we need a move that will bring us to a state that is guaranteed to lose.
Is that possible? (Wondering)
 

FAQ: Can Kolya Win at the Stone Pile Game?

Can you explain the rules of the Stone Pile Game?

The Stone Pile Game involves two players taking turns removing stones from a pile. Each player can remove 1, 2, or 3 stones at a time, and the player who removes the last stone wins.

Is it possible for Kolya to win every game of the Stone Pile Game?

No, it is not possible for Kolya to win every game of the Stone Pile Game. The game can be won by either player, depending on their strategy and the starting number of stones in the pile.

What is the optimal strategy for playing the Stone Pile Game?

The optimal strategy for the Stone Pile Game is to always leave your opponent with a multiple of 4 stones. This ensures that you will always have a winning move, no matter what your opponent does.

Can the Stone Pile Game be played with more than two players?

Yes, the Stone Pile Game can be played with more than two players. In this case, the players take turns removing stones from one large shared pile, and the last player to make a move wins.

Are there any variations of the Stone Pile Game?

Yes, there are variations of the Stone Pile Game. Some variations include changing the number of stones that can be removed at a time, or adding a rule that players must take turns removing stones from different piles. These variations can change the optimal strategy for winning the game.

Similar threads

MHB Winning Strategy for "The Connected Game
Replies
1
Views
2K
How Can You Calculate Winning Probabilities in a Game with T's, D's, and I's?
Replies
4
Views
2K
B Validating Darts Tournament Skill Levels: A Non-Intrusive Approach
Replies
4
Views
1K
Help finding winning strategies in the following tile game?
Replies
2
Views
2K
MHB Pebble Challenge: Who Wins & Why?
Replies
1
Views
2K
Comp Sci Designing HTML+CSS for 23 toothpicks game
Replies
4
Views
1K
Enjoyable Enigmas #2: Who Wins the Matchstick Game?
Replies
7
Views
2K
Help creating a ranking system
Replies
2
Views
1K
MHB Probability of winning at least two games in a row - - - Elementary Probability
Replies
1
Views
9K
I Can Angular Velocity Accurately Control Ragdoll Limbs in Game Physics?
Replies
5
Views
1K

Hot Threads

Recent Insights

Back
Top