Problem Solving Strategies

Math.  A little word that strikes fear among so many students.  A jumble of numbers and letters in a problem and you don’t know how to solve it.  Here are some strategies you can use when trying to solve a math problem.

1. Guess and check

2. Make an orderly list

3. Draw a diagram

4.    Look for a pattern

5.    Make a table

6.    Consider special cases

7.    Use a variable/Use two variables

8.    Work backwards

9.    Eliminate possibilities

10. The pigeonhole principle

11. Inductive reasoning

12. Deductive reasoning

Most strategies listed seem pretty self-explanatory.  But what is the pigeonhole principle?  I don’t remember learning about that in school.

By definition, the pigeonhole principle state, if m pigeons are placed into n pigeonholes and m > n, then there must be at least two pigeons in one pigeonhole. 

Example 1

If we have 10 pigeons and 9 pigeon holes, then m=10 and n=9.  Therefore 10 > 9 so there must be at least two pigeons in one pigeonhole.

Example 2

If we have 26 pigeons and 25 holes, then m =26 and n=25.  Therefore, 26 > 25 so again there must be at least two pigeons in one pigeonhole.

Example 3

If we have 7 pigeons and 9 pigeonholes, then m=7 and n=9.  Therefore, 7 < 9 and the pigeons can each have their own hole. 

See, math isn’t so hard!  The pigeonhole principle seems pretty simple to understand.  If you don’t have enough space somebody has to share.  Peter Gustav Lejeune Dirichlet is believed to be the first to formulate this idea.  Click on the links to learn more about Peter Gustav Lejeune Dirichelt and the pigeonhole principle.