Difference between revisions of "1997 AIME Problems/Problem 10"

 
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== Problem ==
 
== Problem ==
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Every card in a deck has a picture of one shape - circle, square, or triangle, which is painted in one of the three colors - red, blue, or green. Furthermore, each color is applied in one of three shades - light, medium, or dark. The deck has 27 cards, with every shape-color-shade combination represented. A set of three cards from the deck is called complementary if all of the following statements are true:
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i. Either each of the three cards has a different shape or all three of the card have the same shape.
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ii. Either each of the three cards has a different color or all three of the cards have the same color.
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iii. Either each of the three cards has a different shade or all three of the cards have the same shade.
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How many different complementary three-card sets are there?
  
 
== Solution ==
 
== Solution ==
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{{solution}}
  
 
== See also ==
 
== See also ==
* [[1997 AIME Problems]]
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{{AIME box|year=1997|num-b=9|num-a=11}}

Revision as of 15:34, 20 November 2007

Problem

Every card in a deck has a picture of one shape - circle, square, or triangle, which is painted in one of the three colors - red, blue, or green. Furthermore, each color is applied in one of three shades - light, medium, or dark. The deck has 27 cards, with every shape-color-shade combination represented. A set of three cards from the deck is called complementary if all of the following statements are true:

i. Either each of the three cards has a different shape or all three of the card have the same shape.

ii. Either each of the three cards has a different color or all three of the cards have the same color.

iii. Either each of the three cards has a different shade or all three of the cards have the same shade.

How many different complementary three-card sets are there?

Solution

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See also

1997 AIME (ProblemsAnswer KeyResources)
Preceded by
Problem 9
Followed by
Problem 11
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
All AIME Problems and Solutions
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