2000 USAMO Problems/Problem 3: Difference between revisions
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=== Problem | === Problem === | ||
A game of solitaire is played with <math>R</math> red cards, <math>W</math> white cards, and <math>B</math> blue cards. A player plays all the cards one at a time. With each play he accumulates a penalty. If he plays a blue card, then he is charged a penalty which is the number of white cards still in his hand. If he plays a white card, then he is charged a penalty which is twice the number of red cards still in his hand. If he plays a red card, then he is charged a penalty which is three times the number of blue cards still in his hand. Find, as a function of <math>R, W,</math> and <math>B,</math> the minimal total penalty a player can amass and all the ways in which this minimum can be achieved. | A game of solitaire is played with <math>R</math> red cards, <math>W</math> white cards, and <math>B</math> blue cards. A player plays all the cards one at a time. With each play he accumulates a penalty. If he plays a blue card, then he is charged a penalty which is the number of white cards still in his hand. If he plays a white card, then he is charged a penalty which is twice the number of red cards still in his hand. If he plays a red card, then he is charged a penalty which is three times the number of blue cards still in his hand. Find, as a function of <math>R, W,</math> and <math>B,</math> the minimal total penalty a player can amass and all the ways in which this minimum can be achieved. | ||
Revision as of 13:40, 22 April 2012
Problem
A game of solitaire is played with 
red cards, 
white cards, and 
blue cards. A player plays all the cards one at a time. With each play he accumulates a penalty. If he plays a blue card, then he is charged a penalty which is the number of white cards still in his hand. If he plays a white card, then he is charged a penalty which is twice the number of red cards still in his hand. If he plays a red card, then he is charged a penalty which is three times the number of blue cards still in his hand. Find, as a function of 
and 
the minimal total penalty a player can amass and all the ways in which this minimum can be achieved.
