Dirichlet's principle, also known as the drawer (distribution) principle in its most general formulation states:
Suppose that several objects are arranged in drawers. If there are more items than drawers, then at least one drawer has more than one item.
Example Problem:
There are 367 fourth graders in a school. Will there be at least two of them who were born on the same date?
Solution:
Dirichlet's principle:
If we have more "objects" (in this case children) than "places" (in this case possible dates of birth), then at least one place must have more than one object.
Application of the principle:
There are 365 days in a calendar year (if the year is not a leap year), or 366 days (if it is a leap year). In the problem we have 367 fourth graders, even if all the children were born on different days, there would still be more children than days in the year. Therefore, at least two students will have a birthday on the same date.
Conclusion:
Yes, there will be at least two fourth graders who were born on the same date.
Answer: YES
