Difference between revisions of "2000 USAMO Problems/Problem 3"
m |
(Added See Also) |
||
| Line 2: | Line 2: | ||
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. | ||
| + | |||
| + | == See also == | ||
| + | {{USAMO newbox|year=2000|num-b=2|num-a=4}} | ||
| + | |||
| + | [[Category:Olympiad Algebra Problems]] | ||
Revision as of 13:41, 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.
See also
| 2000 USAMO (Problems • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 1 • 2 • 3 • 4 • 5 • 6 | ||
| All USAMO Problems and Solutions | ||
