The Birthday Party Problem

 

Betty’s friends threw her a birthday party. Everyone (including Betty) met exactly 3 new people at the party. 

When Betty told her mom about the party later, her mom said, “That sounds like fun! How many people were there at the party?” 

“I think there were 14, or maybe 15, including me,” answered Betty.

Question: If Betty was right that there were either 14 or 15 people at the party, then which number is correct? 

For the solution, click "Read More" below.

The Isosceles Triangle Problem

The lines below are parallel. 

If we place a point on the top line, we can connect that point to points A and B to create an isosceles triangle:  (Remember -- an isosceles triangle has two sides of the same length.)

Question:  How many other ways can this be done?  How many distinct isosceles triangles can you make that include points A and B as two of the three vertices?

For the solution, click "Read More" below.