Hi

[mathisfun]

I have a problem for y'all
In each round of a game played with tokens, the player with the most tokens gives one token to each of the other players and discards one. The game ends when any player runs out of tokens. Natalie has 15 tokens, Jon has 14; and Ryan has 13. How many rounds will be in the game and who is the first to lose all the tokens.

 

[Matt]

Surely you can simulate the game on a piece of paper...

 

[Denis]

I have a problem for y'all
In each round of a game played with tokens, the player with the most tokens gives one token to each of the other players and discards one. The game ends when any player runs out of tokens. Natalie has 15 tokens, Jon has 14; and Ryan has 13. How many rounds will be in the game and who is the first to lose all the tokens.

AS Matt says, get started on paper:
N. J. R.
15 14 13*
12 15 14
13 12 15
14 13 12*
continue for a few and notice what happens every 3rd time (*);
then you'll be able to "project" to the end...

 

[mathisfun]

Lets see 36 rounds and ryan will be the one to lose all of his tokens?

 

[mathisfun]

bump? is that the right answer?

 

[Gene]

Very close. If 15 14 13 is the 1st turn, and 14 13 12 the 4th, I think the 36th and 37th turns are
N J R
2 1 4
3 2 1
-----------------
Gene

 

[mathisfun]

oh ok well thanks man

 

[TchrWill]

The transfers result in the following pattern:
15-14-13
12-15-14
13-12-15
14-13-12
11-14-13
12-11-14
13-12-11

Clearly, it will tale 12 x 3 - 36 transfers to reach the holdings of 3-2-1
On the 37th transfer, Natalie ends up with zero tokens.