Difference between revisions of "2025 AIME I Problems/Problem 3"
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==Problem== | ==Problem== | ||
| − | The <math>9</math> members of a baseball team went to an ice-cream parlor after their game. Each player had a | + | The <math>9</math> members of a baseball team went to an ice-cream parlor after their game. Each player had a single scoop cone of chocolate, vanilla, or strawberry ice cream. At least one player chose each flavor, and the number of players who chose chocolate was greater than the number of players who chose vanilla, which was greater than the number of players who chose strawberry. Let <math>N</math> be the number of different assignments of flavors to players that meet these conditions. Find the remainder when <math>N</math> is divided by <math>1000.</math> |
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| + | ==See also== | ||
| + | {{AIME box|year=2025|num-b=1|num-a=3|n=I}} | ||
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| + | {{MAA Notice}} | ||
Revision as of 19:29, 13 February 2025
Problem
The 
members of a baseball team went to an ice-cream parlor after their game. Each player had a single scoop cone of chocolate, vanilla, or strawberry ice cream. At least one player chose each flavor, and the number of players who chose chocolate was greater than the number of players who chose vanilla, which was greater than the number of players who chose strawberry. Let 
be the number of different assignments of flavors to players that meet these conditions. Find the remainder when is divided by 
See also
| 2025 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
