2008 UNCO Math Contest II Problems/Problem 1
Problem
Determine the number of square arrays whose row and column sums are equal to , using as entries. Entries may be repeated, and not all of need be used as the two examples show.
Solution
Case 1: The numbers include
Row 1:
Row 2:
Row 3:
There are 3 rows to choose where to place Row 2, giving us cases.
Case 2: The numbers include
Row 1:
Row 2:
Row 3:
There are 3 rows to choose where to place Row 2, giving us cases.
Case 3: The numbers include
Row 1:
Row 2:
Row 3:
There are 3 rows to choose where to place Row 2, giving us cases.
Case 4: The numbers include
Row 1:
Row 2:
Row 3:
There are 3 rows to choose where to place Row 2, and Row 1 can go on either top or bottom, giving us cases.
Case 5: The numbers include
Row 1:
Row 2:
Row 3:
There are 3 rows to choose where to place Row 2, and Row 1 can go on either top or bottom, giving us cases.
This gives us a total of ways.
See Also
2008 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
Preceded by First Question |
Followed by Problem 2 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
All UNCO Math Contest Problems and Solutions |