# Problem of the Month - May/June 2020

George Polya, a mathematician from Stanford, said, "a problem is not a problem if you can solve it in 24 hours."  His statement indicates that if you solve a problem in less than a day it usually is a problem that is similar to one that you have solved before.  However, in our adult lives, a problem is something that you encounter, where you may or may not have an idea of where to start.

So let's dive into this month's problem:

Level A:

Amy had a barbecue.  She invited two guests.  Her guests each invited four guests, and then those guests each invited three guests.

How many people were at Amy's barbecue?

Explain how you determined your solution.  Remember to post images on this board go to postimages.org and create a link then use the picture icon and post the link in there.

Level B:

At Amber's barbecue 1/4 of the people had long hair.  One-half of the people at the barbecue were boys, 1/4 of the girls had short blond hair.  None of the boys had long hair.

If there were 32 guests at the barbecue, what is the maximum number of girls who had short red hair?

Show how you determined your answer and why you know you have a correct solution. Remember to post images on this board go to postimages.org and create a link then use the picture icon and post the link in there.

Level C:

Mark, Connie, Heidi, Sarah, Patricia, and Eric are all going to a costume party.  Figure out which person is wearing what costume and when they arrived at the party.

• The person that arrived fourth was wearing a bathing suit.
• Sarah was the last to arrive
• Connie and Mark arrived and stayed together.
• The first person was dressed as a French Maid.
• Superman arrived right before Sarah
• The Potato Heads were always together at the party.
• Patricia was a Surfer Dude.
• The French Maid was not Heidi.
• The Vampire arrived after Superman.

Show how you determined your answer and why you know you have a correct solution. Remember to post images on this board go to postimages.org and create a link then use the picture icon and post the link in there.

Level D:

Your Aunt is having a baby.  You have created a party game for a baby. show.  It is called pick the gender.  You put pink and blue tiles into a bag.  You asked two guests to pick one tile out of the bag without looking.  You tell your guests that if they are the same color, player A wins and if they are two different colors, then player B wins.

How many tiles of which colors did you put into the bag to make sure that both players have an equal chance of winning?

Explain your solution and why it is fair.

Level E:

A man and his spouse invite 5 other couples to a dinner party.  As the guests arrive for drinks before dinner, they shake hands.  Not everybody shakes everybody's hands, and of course no one shakes hands with his own spouse.  Later, as they sit down to dinner, the host asks each other person, including his spouse, "how many hands you shake?" He notices, to his surprise that each respondent shook a different number of hands.

How many did his spouse shake?

Explain your solution and justify your reasoning. Remember to post images on this board go to postimages.org and create a link then use the picture icon and post the link in there.

Source: insidemathematics.org