Difference between revisions of "2016 UNCO Math Contest II Problems/Problem 9"
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== Problem == | == Problem == | ||
| + | Chess Masters | ||
| + | |||
| + | (This should not be in intermediate combinatorics; it makes use of some very obvious basic knowledge of combinatorics) | ||
| + | Four identical white pawns and four identical black pawns are to be placed on a standard | ||
| + | 8 × 8, two-colored chessboard. | ||
| + | |||
| + | How many distinct arrangements of the colored pawns on the colored board are possible? | ||
| + | |||
| + | No two pawns occupy the same square. The color of a pawn need not match the color of the square it occupies, but it might. | ||
| + | You may give your answer as a formula involving factorials or combinations: you are not asked to compute the number. | ||
== Solution == | == Solution == | ||
| + | There are <math>\frac{64!}{56!4!4!}</math> arrangements of the colored pawns on the standard board. | ||
== See also == | == See also == | ||
{{UNCO Math Contest box|year=2016|n=II|num-b=8|num-a=10}} | {{UNCO Math Contest box|year=2016|n=II|num-b=8|num-a=10}} | ||
| − | [[Category:]] | + | [[Category: Intermediate Combinatorics Problems]] |
Latest revision as of 15:46, 17 October 2023
Problem
Chess Masters
(This should not be in intermediate combinatorics; it makes use of some very obvious basic knowledge of combinatorics) Four identical white pawns and four identical black pawns are to be placed on a standard 8 × 8, two-colored chessboard.
How many distinct arrangements of the colored pawns on the colored board are possible?
No two pawns occupy the same square. The color of a pawn need not match the color of the square it occupies, but it might. You may give your answer as a formula involving factorials or combinations: you are not asked to compute the number.
Solution
There are 
arrangements of the colored pawns on the standard board.
See also
| 2016 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 8 |
Followed by Problem 10 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
| All UNCO Math Contest Problems and Solutions | ||
