Difference between revisions of "2010 AMC 10B Problems/Problem 23"
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==Notes== | ==Notes== | ||
| − | There is a general formula (coming from the fields of [[combinatorics]] and [[representation theory]]) to answer problems of this form; it is known as the [http://en.wikipedia.org/wiki/Young_tableau#Dimension_of_a_representation hook-length formula]. This formula gives the answer of <math>42</math>. | + | There is a general formula (coming from the fields of [[combinatorics]] and [[representation theory]]) to answer problems of this form; it is known as the [http://en.wikipedia.org/wiki/Young_tableau#Dimension_of_a_representation hook-length formula]. This formula gives the answer of <math>42 </math>. |
== See also == | == See also == | ||
{{AMC10 box|year=2010|ab=B|num-b=22|num-a=24}} | {{AMC10 box|year=2010|ab=B|num-b=22|num-a=24}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 16:55, 4 August 2014
Problem
The entries in a 
array include all the digits from 1 through 9, arranged so that the entries in every row and column are in increasing order. How many such arrays are there?
Notes
There is a general formula (coming from the fields of combinatorics and representation theory) to answer problems of this form; it is known as the hook-length formula. This formula gives the answer of 
.
See also
| 2010 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 22 |
Followed by Problem 24 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
