Casework

In combinatorics, casework is a counting method where one splits a problem into several parts, counts these cases individually, then adds together each part's total. While there are problems where casework produces the most elegant solution, in those where a shorter answer exists, casework may be considered brute force.

Videos

• AoPS Casework Counting Part 1
• AoPS Casework Counting Part 2

Example Problems and Solutions

Introductory

• 2006 AMC 12A Problem 20

• 2005 AMC 10A Problem 14

Intermediate

• 2004 AIME 2 Problem 2
• 2004 AIME 2 Problem 4
• 2005 AIME 1 Problem 5
• 2000 AIME 1 Problem 5

See also

• Complementary counting
• Constructive counting
• Overcounting