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A game is played with tokens according to the following rule. In each

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Joined: 02 Nov 2018
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A game is played with tokens according to the following rule. In each  [#permalink]

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New post 18 Mar 2019, 02:46
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Difficulty:

  65% (hard)

Question Stats:

40% (02:40) correct 60% (03:14) wrong based on 15 sessions

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A game is played with tokens according to the following rule. In each round, the player with the most tokens gives one token to each of the other players and also places one token into a discard pile. The game ends when some player runs out of tokens. Players A, B, and C start with 15, 14, and 13 tokens, respectively.
How many rounds will there be in the game?

(A) 36

(B) 37

(C) 38

(D) 39

(E) 40
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Joined: 02 Aug 2009
Posts: 8283
Re: A game is played with tokens according to the following rule. In each  [#permalink]

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New post 18 Mar 2019, 06:24
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Noshad wrote:
A game is played with tokens according to the following rule. In each round, the player with the most tokens gives one token to each of the other players and also places one token into a discard pile. The game ends when some player runs out of tokens. Players A, B, and C start with 15, 14, and 13 tokens, respectively.
How many rounds will there be in the game?

(A) 36

(B) 37

(C) 38

(D) 39

(E) 40



Two methods..

(I) Total are 15+14+13=42, and the last game would contain 3+2+1=6..
So discarded are 42-6=36, ans as 1 gets discarded in every game, we require 36 games till last game...
so last game has 3, 2, 1.. it will become 0,3,2 and game gets over, so 36+1=37

(II) Let us see what happens in each game till we get a PATTERN
Game ---A-----B----C----Discarded
start----15----14----13---0
(1)------12----15----14---1
(2)------13----12-----15--2
(3)------14......13.....12....3
and so on

so in 3 games all will lose 1 each..
so 15-14-13 will become 3-2-1 in (15-3)*3=12*3=36 games
in the final game A-B-C will become 0-3-2
so 36+1=37 games

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Re: A game is played with tokens according to the following rule. In each   [#permalink] 18 Mar 2019, 06:24
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