# Individual Research Projects Section 3.5

### Project 3.6 Convention Problem

A mathematician attended a convention of men and women scientists. The mathematician observed that if any two of them were picked at random, at least one of the two would be male. From this information, it is possible to deduce what percentage of the attendees were women?

### Project 3.7 Present Problem

Happy Harry wrapped up a present for his wife, and he put a gift inside a small box. He then put this box inside a second box, and then placed the second box inside a third. He completed his task by butting the third box inside a larger fourth box. He tells his wife she can have the present, but only if she can identify the order of the boxes before opening them. Harry gives the following clues:

Clue 1: The boxes (in no particular order are red, blue, gold, and black.
Clue 2: The gold box is not inside the blue box.
Clue 3: The blue box is inside two other boxes.
Clue 4: The black box is bigger than the red box, but smaller than the gold box.

Can you figure out the order of the boxes from smallest (first) to the largest (fourth)?

### Project 3.8 Convention Problem

A mathematician attended a convention of men and women scientists. The mathematician observed that if any two of them were picked at random, at least one of the two would be male. From this information, it is possible to deduce what percentage of the attendees were women?